Method and system for  patient-specific modeling of blood flow

ABSTRACT

Embodiments include a system for determining cardiovascular information for a patient. The system may include at least one computer system configured to receive patient-specific data regarding a geometry of the patient&#39;s heart, and create a three-dimensional model representing at least a portion of the patient&#39;s heart based on the patient-specific data. The at least one computer system may be further configured to create a physics-based model relating to a blood flow characteristic of the patient&#39;s heart and determine a fractional flow reserve within the patient&#39;s heart based on the three-dimensional model and the physics-based model.

PRIORITY

This application claims the benefit of priority from U.S. ProvisionalApplication No. 61/401,462, filed Aug. 12, 2010, U.S. ProvisionalApplication No. 61/401,915, filed Aug. 20, 2010, U.S. ProvisionalApplication No. 61/402,308, filed Aug. 26, 2010, U.S. ProvisionalApplication No. 61/402,345, filed Aug. 27, 2010, and U.S. ProvisionalApplication No. 61/404,429, filed Oct. 1, 2010, which are hereinincorporated by reference in their entirety.

TECHNICAL FIELD

Embodiments include methods and systems for modeling of fluid flow andmore particularly methods and systems for patient-specific modeling ofblood flow.

BACKGROUND

Coronary artery disease may produce coronary lesions in the bloodvessels providing blood to the heart, such as a stenosis (abnormalnarrowing of a blood vessel). As a result, blood flow to the heart maybe restricted. A patient suffering from coronary artery disease mayexperience chest pain, referred to as chronic stable angina duringphysical exertion or unstable angina when the patient is at rest. A moresevere manifestation of disease may lead to myocardial infarction, orheart attack.

A need exists to provide more accurate data relating to coronarylesions, e.g., size, shape, location, functional significance (e.g.,whether the lesion impacts blood flow), etc. Patients suffering fromchest pain and/or exhibiting symptoms of coronary artery disease may besubjected to one or more tests that may provide some indirect evidencerelating to coronary lesions. For example, noninvasive tests may includeelectrocardiograms, biomarker evaluation from blood tests, treadmilltests, echocardiography, single positron emission computed tomography(SPECT), and positron emission tomography (PET). These noninvasivetests, however, typically do not provide a direct assessment of coronarylesions or assess blood flow rates. The noninvasive tests may provideindirect evidence of coronary lesions by looking for changes inelectrical activity of the heart (e.g., using electrocardiography(ECG)), motion of the myocardium (e.g., using stress echocardiography),perfusion of the myocardium (e.g., using PET or SPECT), or metabolicchanges (e.g., using biomarkers).

For example, anatomic data may be obtained noninvasively using coronarycomputed tomographic angiography (CCTA). CCTA may be used for imaging ofpatients with chest pain and involves using computed tomography (CT)technology to image the heart and the coronary arteries following anintravenous infusion of a contrast agent. However, CCTA also cannotprovide direct information on the functional significance of coronarylesions, e.g., whether the lesions affect blood flow. In addition, sinceCCTA is purely a diagnostic test, it cannot be used to predict changesin coronary blood flow, pressure, or myocardial perfusion under otherphysiologic states, e.g., exercise, nor can it be used to predictoutcomes of interventions.

Thus, patients may also require an invasive test, such as diagnosticcardiac catheterization, to visualize coronary lesions. Diagnosticcardiac catheterization may include performing conventional coronaryangiography (CCA) to gather anatomic data on coronary lesions byproviding a doctor with an image of the size and shape of the arteries.CCA, however, does not provide data for assessing the functionalsignificance of coronary lesions. For example, a doctor may not be ableto diagnose whether a coronary lesion is harmful without determiningwhether the lesion is functionally significant. Thus, CCA has led towhat has been referred to as an “oculostenotic reflex” of someinterventional cardiologists to insert a stent for every lesion foundwith CCA regardless of whether the lesion is functionally significant.As a result, CCA may lead to unnecessary operations on the patient,which may pose added risks to patients and may result in unnecessaryheath care costs for patients.

During diagnostic cardiac catheterization, the functional significanceof a coronary lesion may be assessed invasively by measuring thefractional flow reserve (FFR) of an observed lesion. FFR is defined asthe ratio of the mean blood pressure downstream of a lesion divided bythe mean blood pressure upstream from the lesion, e.g., the aorticpressure, under conditions of increased coronary blood flow, e.g.,induced by intravenous administration of adenosine. The blood pressuresmay be measured by inserting a pressure wire into the patient. Thus, thedecision to treat a lesion based on the determined FFR may be made afterthe initial cost and risk of diagnostic cardiac catheterization hasalready been incurred.

Thus, a need exists for a method for assessing coronary anatomy,myocardial perfusion, and coronary artery flow noninvasively. Such amethod and system may benefit cardiologists who diagnose and plantreatments for patients with suspected coronary artery disease. Inaddition, a need exists for a method to predict coronary artery flow andmyocardial perfusion under conditions that cannot be directly measured,e.g., exercise, and to predict outcomes of medical, interventional, andsurgical treatments on coronary artery blood flow and myocardialperfusion.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the disclosure.

SUMMARY

In accordance with an embodiment, a system for determiningcardiovascular information for a patient includes at least one computersystem configured to receive patient-specific data regarding a geometryof the patient's heart and create a three-dimensional model representingat least a portion of the patient's heart based on the patient-specificdata. The at least one computer system is further configured to create aphysics-based model relating to a blood flow characteristic of thepatient's heart and determine a fractional flow reserve within thepatient's heart based on the three-dimensional model and thephysics-based model.

In accordance with another embodiment, a method for determiningpatient-specific cardiovascular information using at least one computersystem includes inputting into the at least one computer systempatient-specific data regarding a geometry of the patient's heart, andcreating, using the at least one computer system, a three-dimensionalmodel representing at least a portion of the patient's heart based onthe patient-specific data. The method further includes creating, usingthe at least one computer system, a physics-based model relating to ablood flow characteristic of the patient's heart, and determining, usingthe at least one computer system, a fractional flow reserve within thepatient's heart based on the three-dimensional model and thephysics-based model.

In accordance with another embodiment, a non-transitory computerreadable medium for use on at least one computer system containingcomputer-executable programming instructions for performing a method fordetermining patient-specific cardiovascular information is provided. Themethod includes receiving patient-specific data regarding a geometry ofthe patient's heart and creating a three-dimensional model representingat least a portion of the patient's heart based on the patient-specificdata. The method further includes creating a physics-based modelrelating to a blood flow characteristic in the patient's heart anddetermining a fractional flow reserve within the patient's heart basedon the three-dimensional model and the physics-based model.

In accordance with another embodiment, a system for planning treatmentfor a patient includes at least one computer system configured toreceive patient-specific data regarding a geometry of an anatomicalstructure of the patient and create a three-dimensional modelrepresenting at least a portion of the anatomical structure of thepatient based on the patient-specific data. The at least one computersystem is further configured to determine first information regarding ablood flow characteristic within the anatomical structure of the patientbased on the three-dimensional model and a physics-based model relatingto the anatomical structure of the patient, modify the three-dimensionalmodel, and determine second information regarding the blood flowcharacteristic within the anatomical structure of the patient based onthe modified three-dimensional model.

In accordance with another embodiment, a non-transitory computerreadable medium for use on a computer system containingcomputer-executable programming instructions for performing a method forplanning treatment for a patient is provided. The method includesreceiving patient-specific data regarding a geometry of an anatomicalstructure of the patient and creating a three-dimensional modelrepresenting at least a portion of the anatomical structure of thepatient based on the patient-specific data. The method further includesdetermining first information regarding a blood flow characteristicwithin the anatomical structure of the patient based on thethree-dimensional model and a physics-based model relating to theanatomical structure of the patient, and determining second informationregarding the blood flow characteristic within the anatomical structureof the patient based on a desired change in geometry of the anatomicalstructure of the patient.

In accordance with another embodiment, a method for planning treatmentfor a patient using a computer system includes inputting into at leastone computer system patient-specific data regarding a geometry of ananatomical structure of the patient and creating, using the at least onecomputer system, a three-dimensional model representing at least aportion of the anatomical structure of the patient based on thepatient-specific data. The method further includes determining, usingthe at least one computer system, first information regarding a bloodflow characteristic within the anatomical structure of the patient basedon the three-dimensional model and a physics-based model relating to theanatomical structure of the patient. The method also includes modifying,using the at least one computer system, the three-dimensional model, anddetermining, using the at least one computer system, second informationregarding the blood flow characteristic within the anatomical structureof the patient based on the modified three-dimensional model.

In accordance with another embodiment, a system for planning treatmentfor a patient includes at least one computer system configured toreceive patient-specific data regarding a geometry of an anatomicalstructure of the patient and create a three-dimensional modelrepresenting at least a portion of the anatomical structure of thepatient based on the patient-specific data. The at least one computersystem is also configured to determine first information regarding ablood flow characteristic within the anatomical structure of the patientbased on the three-dimensional model and information regarding aphysiological condition of the patient, modify the physiologicalcondition of the patient, and determine second information regarding theblood flow characteristic within the anatomical structure of the patientbased on the modified physiological condition of the patient.

In accordance with another embodiment, a non-transitory computerreadable medium for use on a computer system containingcomputer-executable programming instructions for performing a method forplanning treatment for a patient is provided. The method includesreceiving patient-specific data regarding a geometry of an anatomicalstructure of the patient and creating a three-dimensional modelrepresenting at least a portion of the anatomical structure of thepatient based on the patient-specific data. The method further includesdetermining first information regarding a blood flow characteristicwithin the anatomical structure of the patient based on thethree-dimensional model and information regarding a physiologicalcondition of the patient, and determining second information regardingthe blood flow characteristic within the anatomical structure of thepatient based on a desired change in the physiological condition of thepatient.

In accordance with another embodiment, a method for planning treatmentfor a patient using at least one computer system includes inputting intoat least one computer system patient-specific data regarding a geometryof an anatomical structure of the patient, and creating, using the atleast one computer system, a three-dimensional model representing atleast a portion of the anatomical structure of the patient based on thepatient-specific data. The method also includes determining, using theat least one computer system, first information regarding a blood flowcharacteristic within the anatomical structure of the patient based onthe three-dimensional model and information regarding a physiologicalcondition of the patient. The method further includes modifying, usingthe at least one computer system, the physiological condition of thepatient, and determining, using the at least one computer system, secondinformation regarding the blood flow characteristic within theanatomical structure of the patient based on the modified physiologicalcondition of the patient.

In accordance with another embodiment, a system for determiningpatient-specific cardiovascular information includes at least onecomputer system configured to receive patient-specific data regarding ageometry of an anatomical structure of the patient and create athree-dimensional model representing at least a portion of theanatomical structure of the patient based on the patient-specific data.The at least one computer system is also configured to determine a totalresistance associated with a total flow through the portion of theanatomical structure of the patient and determine information regardinga blood flow characteristic within the anatomical structure of thepatient based on the three-dimensional model, a physics-based modelrelating to the anatomical structure of the patient, and the determinedtotal resistance.

In accordance with another embodiment, a method for determiningpatient-specific cardiovascular information using at least one computersystem includes inputting into the at least one computer systempatient-specific data regarding a geometry of an anatomical structure ofthe patient, and creating, using at least one computer, athree-dimensional model representing at least a portion of theanatomical structure of the patient based on the patient-specific data.The method also includes determining, using at least one computer, atotal resistance associated with a total flow through the portion of theanatomical structure of the patient, and determining, using at least onecomputer, information regarding a blood flow characteristic within theanatomical structure of the patient based on the three-dimensionalmodel, a physics-based model relating to the anatomical structure of thepatient, and the determined total resistance.

In accordance with another embodiment, a non-transitory computerreadable medium for use on a computer system containingcomputer-executable programming instructions for performing a method fordetermining patient-specific cardiovascular information is provided. Themethod includes receiving patient-specific data regarding a geometry ofan anatomical structure of the patient and creating a three-dimensionalmodel representing at least a portion of the anatomical structure of thepatient based on the patient-specific data. The method also includesdetermining a total resistance associated with a total flow through theportion of the anatomical structure of the patient and determininginformation regarding a blood flow characteristic within the anatomicalstructure of the patient based on the three-dimensional model, aphysics-based model relating to the anatomical structure of the patient,and the determined total resistance.

In accordance with another embodiment, a system for providingpatient-specific cardiovascular information using a web site includes atleast one computer system configured to allow a remote user to access aweb site, receive patient-specific data regarding at least a portion ofa geometry of an anatomical structure of the patient, create athree-dimensional model representing at least a portion of theanatomical structure of the patient based on the patient-specific data,and determine information regarding a blood flow characteristic withinthe anatomical structure of the patient based on the three-dimensionalmodel and a physiological condition of the patient. The at least onecomputer system is also configured to communicate display informationregarding a first three-dimensional simulation of at least the portionof the anatomical structure of the patient to the remote user using theweb site. The three-dimensional simulation includes the determinedinformation regarding the blood flow characteristic.

In accordance with another embodiment, a method for providingpatient-specific cardiovascular information using a web site includesallowing, using at least one computer system, a remote user to access aweb site, and receiving, using the at least one computer system,patient-specific data regarding a geometry of an anatomical structure ofthe patient. The method also includes creating, using the at least onecomputer system, a three-dimensional model representing at least aportion of the anatomical structure of the patient based on thepatient-specific data, and determining, using the at least one computersystem, information regarding a blood flow characteristic within theanatomical structure of the patient based on the three-dimensional modeland a physiological condition of the patient. The method furtherincludes communicating, using the at least one computer system, displayinformation regarding a first three-dimensional simulation of at leastthe portion of the anatomical structure of the patient to the remoteuser using the web site. The three-dimensional simulation includes thedetermined information regarding the blood flow characteristic.

In accordance with another embodiment, a non-transitory computerreadable medium for use on a computer system containingcomputer-executable programming instructions for performing a method forproviding patient-specific cardiovascular information using a web siteis provided. The method includes allowing a remote user to access a website, receiving patient-specific data regarding a geometry of ananatomical structure of the patient, and creating a three-dimensionalmodel representing at least a portion of the anatomical structure of thepatient based on the patient-specific data. The method also includesdetermining information regarding a blood flow characteristic within theanatomical structure of the patient based on the three-dimensional modeland a physics-based model relating to the anatomical structure of thepatient, and communicating display information regarding a firstthree-dimensional simulation of at least the portion of the anatomicalstructure of the patient to the remote user using the web site. Thethree-dimensional simulation includes the determined informationregarding the blood flow characteristic.

In accordance with another embodiment, a system for determiningpatient-specific time-varying cardiovascular information includes atleast one computer system configured to receive time-varyingpatient-specific data regarding a geometry of at least a portion of ananatomical structure of the patient at different times and create athree-dimensional model representing at least a portion of theanatomical structure of the patient based on the patient-specific data.The at least one computer system is also configured to determineinformation regarding a change in a blood flow characteristic over timewithin the anatomical structure of the patient based on thethree-dimensional model and a physics-based model relating to theanatomical structure of the patient.

In accordance with another embodiment, a method for determiningpatient-specific time-varying cardiovascular information using at leastone computer system includes receiving, using at least one computersystem, time-varying patient-specific data regarding a geometry of ananatomical structure of the patient at different times. The method alsoincludes creating, using the at least one computer system, athree-dimensional model representing at least a portion of theanatomical structure of the patient based on the patient-specific data.The method further includes determining, using the at least one computersystem, information regarding a change in a blood flow characteristicover time within the anatomical structure of the patient based on thethree-dimensional model and the information regarding a physics-basedmodel relating to the anatomical structure of the patient.

In accordance with another embodiment, a non-transitory computerreadable medium for use on a computer system containingcomputer-executable programming instructions for performing a method fordetermining patient-specific time-varying cardiovascular information isprovided. The method includes receiving time-varying patient-specificdata regarding a geometry of an anatomical structure of the patient atdifferent times, creating a three-dimensional model representing atleast a portion of the anatomical structure of the patient based on thepatient-specific data, and determining information regarding a change ina blood flow characteristic over time within the anatomical structure ofthe patient based on the three-dimensional model and the informationregarding a physics-based model relating to the anatomical structure ofthe patient.

In accordance with another embodiment, a system for determiningcardiovascular information for a patient includes at least one computersystem configured to receive patient-specific data regarding a geometryand at least one material property of at least a portion of ananatomical structure of the patient. The anatomical structure includesat least a portion of a blood vessel. The at least one computer systemis further configured to create a three-dimensional model representingthe anatomical structure of the patient based on the patient-specificdata, and determine information regarding a blood flow characteristicwithin the anatomical structure of the patient based on thethree-dimensional model and a physiological condition of the patient.The at least one computer system is also configured to identify alocation of a plaque within the blood vessel.

In accordance with another embodiment, a method for determiningcardiovascular information for a patient using at least one computersystem includes receiving, using at least one computer system,patient-specific data regarding a geometry and at least one materialproperty of at least a portion of an anatomical structure of thepatient. The anatomical structure includes at least a portion of a bloodvessel. The method also includes creating, using the at least onecomputer system, a three-dimensional model representing the anatomicalstructure of the patient based on the patient-specific data, anddetermining, using the at least one computer system, informationregarding a blood flow characteristic within the anatomical structure ofthe patient based on the three-dimensional model and a physiologicalcondition of the patient. The method further includes identifying, usingthe at least one computer system, a plaque within the blood vessel.

In accordance with another embodiment, a non-transitory computerreadable medium for use on a computer system containingcomputer-executable programming instructions for performing a method fordetermining cardiovascular information for a patient is provided. Themethod includes receiving patient-specific data regarding a geometry andat least one material property of at least a portion of an anatomicalstructure of the patient. The anatomical structure includes at least aportion of a blood vessel. The method also includes creating athree-dimensional model representing the anatomical structure of thepatient based on the patient-specific data, determining informationregarding a blood flow characteristic within the anatomical structure ofthe patient based on the three-dimensional model and a physiologicalcondition of the patient, and identifying a location of a plaque withinthe blood vessel.

In accordance with another embodiment, a system for determiningcardiovascular information for a patient includes at least one computersystem configured to receive patient-specific data regarding a geometryof at least a portion of an anatomical structure of the patient. Theanatomical structure includes at least a portion of a plurality ofarteries and tissue connected to at least a portion of the plurality ofarteries. The at least one computer system is further configured tocreate a three-dimensional model representing the anatomical structureof the patient based on the patient-specific data, divide at least aportion of the three-dimensional model representing the tissue intosegments, and determine information regarding a blood flowcharacteristic associated with at least one of the segments based on thethree-dimensional model and a physiological condition of the patient.

In accordance with another embodiment, a method for determiningcardiovascular information for a patient using at least one computersystem includes receiving, using at least one computer system,patient-specific data regarding a geometry of at least a portion of ananatomical structure of the patient. The anatomical structure includesat least a portion of a plurality of arteries and tissue connected to atleast a portion of the plurality of arteries. The method also includescreating, using the at least one computer system, a three-dimensionalmodel representing the anatomical structure of the patient based on thepatient-specific data, and extending, using the at least one computersystem, the three-dimensional model to form an augmented model. Themethod further includes dividing, using the at least one computersystem, at least a portion of the augmented model representing thetissue into segments, and determining, using the at least one computersystem, information regarding a blood flow characteristic associatedwith at least one of the segments based on the augmented model and aphysiological condition of the patient.

In accordance with another embodiment, a non-transitory computerreadable medium for use on a computer system containingcomputer-executable programming instructions for performing a method fordetermining cardiovascular information for a patient is provided. Themethod includes receiving patient-specific data regarding a geometry ofat least a portion of an anatomical structure of the patient. Theanatomical structure includes at least a portion of a plurality ofarteries and tissue connected to at least a portion of the plurality ofarteries. The method also includes creating a three-dimensional modelrepresenting the anatomical structure of the patient based on thepatient-specific data, dividing at least a portion of thethree-dimensional model representing the tissue into segments, anddetermining information regarding a blood flow characteristic associatedwith at least one of the segments based on the three-dimensional modeland a physics-based model relating to the anatomical structure.

In accordance with another embodiment, a system for determiningcardiovascular information for a patient includes at least one computersystem configured to receive patient-specific data regarding a geometryof the patient's brain. The at least one computer system is furtherconfigured to create a three-dimensional model representing at least aportion of the patient's brain based on the patient-specific data, anddetermine information regarding a blood flow characteristic within thepatient's brain based on the three-dimensional model and a physics-basedmodel relating to the patient's brain.

In accordance with another embodiment, a method for determiningpatient-specific cardiovascular information using at least one computersystem includes inputting into the at least one computer systempatient-specific data regarding a geometry of at least a portion of aplurality of cerebral arteries of the patient. The method also includescreating, using the at least one computer system, a three-dimensionalmodel representing at least the portion of the cerebral arteries of thepatient based on the patient-specific data, and determining, using theat least one computer system, information regarding a blood flowcharacteristic within the cerebral arteries of the patient based on thethree-dimensional model and a physics-based model relating to thecerebral arteries of the patient.

In accordance with another embodiment, a non-transitory computerreadable medium for use on at least one computer system containingcomputer-executable programming instructions for performing a method fordetermining patient-specific cardiovascular information is provided. Themethod includes receiving patient-specific data regarding a geometry ofthe patient's brain, creating a three-dimensional model representing atleast a portion of the patient's brain based on the patient-specificdata, and determining information regarding a blood flow characteristicwithin the patient's brain based on the three-dimensional model and aphysics-based model relating to the patient's brain.

Additional embodiments and advantages will be set forth in part in thedescription which follows, and in part will be obvious from thedescription, or may be learned by practice of the disclosure. Theembodiments and advantages will be realized and attained by means of theelements and combinations particularly pointed out below.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate several embodiments and togetherwith the description, serve to explain the principles of the disclosure.

FIG. 1 is a schematic diagram of a system for providing variousinformation relating to coronary blood flow in a specific patient,according to an exemplary embodiment;

FIG. 2 is a flow chart of a method for providing various informationrelating to blood flow in a specific patient, according to an exemplaryembodiment;

FIG. 3 is a flow chart showing the substeps of the method of FIG. 2;

FIG. 4 shows imaging data obtained noninvasively from a patient,according to an exemplary embodiment;

FIG. 5 shows an exemplary three-dimensional model generated using theimaging data of FIG. 4;

FIG. 6 shows a portion of a slice of the imaging data of FIG. 4including seeds for forming a first initial model;

FIG. 7 shows a portion of the first initial model formed by expandingthe seeds of FIG. 6;

FIG. 8 shows a trimmed solid model, according to an exemplaryembodiment;

FIG. 9 shows an exemplary computed FFR (cFFR) model when the patient isat rest;

FIG. 10 shows an exemplary cFFR model when the patient is under maximumhyperemia;

FIG. 11 shows an exemplary cFFR model when the patient is under maximumexercise;

FIG. 12 shows a portion of a trimmed solid model provided for forming alumped parameter model, according to an exemplary embodiment;

FIG. 13 shows a portion of the centerlines for the trimmed solid modelof FIG. 12, provided for forming a lumped parameter model;

FIG. 14 shows segments formed based on the trimmed solid model of FIG.12, provided for forming a lumped parameter model;

FIG. 15 shows the segments of FIG. 14 replaced by resistors, providedfor forming a lumped parameter model;

FIG. 16 shows exemplary lumped parameter models representing theupstream and downstream structures at the inflow and outflow boundariesof a solid model, according to an exemplary embodiment;

FIG. 17 shows a three-dimensional mesh prepared based on the solid modelof FIG. 8;

FIGS. 18 and 19 show portions of the three-dimensional mesh of FIG. 17;

FIG. 20 shows a model of the patient's anatomy including blood flowinformation with certain points on the model identified by individualreference labels;

FIG. 21 is a graph of simulated blood pressure over time in the aortaand at some of the points identified in FIG. 20;

FIG. 22 is a graph of simulated blood flow over time at each of thepoints identified in FIG. 20;

FIG. 23 is a finalized report, according to an exemplary embodiment;

FIG. 24 is a flow chart of a method for providing various informationrelating to coronary blood flow in a specific patient, according to anexemplary embodiment;

FIG. 25 shows a modified cFFR model determined based on a solid modelcreated by widening a portion of the left anterior descending (LAD)artery and a portion of the LCX artery, according to an exemplaryembodiment;

FIG. 26 shows an example of a modified simulated blood flow model afterwidening a portion of the LAD artery and a portion of the leftcircumflex (LCX) artery, according to an exemplary embodiment;

FIG. 27 is a flow chart of a method for simulating various treatmentoptions using a reduced order model, according to an exemplaryembodiment;

FIG. 28 is a flow chart of a method for simulating various treatmentoptions using a reduced order model, according to another exemplaryembodiment;

FIG. 29 is a flow chart of a method for providing various informationrelating to myocardial perfusion in a specific patient, according to anexemplary embodiment;

FIG. 30 is a flow chart of a method for providing various informationrelating to myocardial perfusion in a specific patient, according toanother exemplary embodiment;

FIG. 31 shows a patient-specific model providing various informationrelating to myocardial perfusion, according to an exemplary embodiment;

FIG. 32 is a flow chart of a method for providing various informationrelating to myocardial perfusion in a specific patient, according to afurther exemplary embodiment;

FIG. 33 is a cross-sectional view of plaque built up along a bloodvessel wall;

FIG. 34 shows a patient-specific model providing various informationrelating to plaque vulnerability, according to an exemplary embodiment;

FIG. 35 is a flow chart of a method for providing various informationrelating to assessing plaque vulnerability, myocardial volume risk, andmyocardial perfusion risk in a specific patient, according to anexemplary embodiment;

FIG. 36 is a schematic diagram showing information obtained from themethod of FIG. 35, according to an exemplary embodiment;

FIG. 37 is a diagram of cerebral arteries;

FIG. 38 is a flow chart of a method for providing various informationrelating to intracranial and extracranial blood flow in a specificpatient, according to an exemplary embodiment;

FIG. 39 is a flow chart of a method for providing various informationrelating to cerebral perfusion in a specific patient, according to anexemplary embodiment;

FIG. 40 is a flow chart of a method for providing various informationrelating to cerebral perfusion in a specific patient, according toanother exemplary embodiment;

FIG. 41 is a flow chart of a method for providing various informationrelating to cerebral perfusion in a specific patient, according to afurther exemplary embodiment; and

FIG. 42 is a flow chart of a method for providing various informationrelating to assessing plaque vulnerability, cerebral volume risk, andcerebral perfusion risk in a specific patient, according to an exemplaryembodiment.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to exemplary embodiments, examplesof which are illustrated in the accompanying drawings. Whereverpossible, the same reference numbers will be used throughout thedrawings to refer to the same or like parts. This description isorganized according to the following outline:

-   -   I. Overview    -   II. Obtaining and Preprocessing Patient-Specific Anatomical Data    -   III. Creating The Three-Dimensional Model Based On Obtained        Anatomical Data    -   IV. Preparing The Model For Analysis and Determining Boundary        Conditions        -   A. Preparing the Model For Analysis        -   B. Determining Boundary Conditions            -   i. Determining Reduced Order Models            -   ii. Exemplary Lumped Parameter Models        -   C. Creating the Three-Dimensional Mesh    -   V Performing The Computational Analysis And Outputting Results        -   A. Performing the Computational Analysis        -   B. Displaying Results for Blood Pressure, Flow, and cFFR        -   C. Verifying Results        -   D. Another Embodiment of a System and Method for Providing            Coronary Blood Flow Information    -   VI. Providing Patient-Specific Treatment Planning        -   A. Using Reduced Order Models to Compare Different Treatment            Options    -   VII. Other Results        -   A. Assessing Myocardial Perfusion        -   B. Assessing Plaque Vulnerability    -   VIII. Other Applications        -   A. Modeling Intracranial and Extracranial Blood Flow            -   i. Assessing Cerebral Perfusion            -   ii. Assessing Plaque Vulnerability

I. Overview

In an exemplary embodiment, a method and system determines variousinformation relating to blood flow in a specific patient usinginformation retrieved from the patient noninvasively. The determinedinformation may relate to blood flow in the patient's coronaryvasculature. Alternatively, as will be described below in furtherdetail, the determined information may relate to blood flow in otherareas of the patient's vasculature, such as carotid, peripheral,abdominal, renal, and cerebral vasculature. The coronary vasculatureincludes a complex network of vessels ranging from large arteries toarterioles, capillaries, venules, veins, etc. The coronary vasculaturecirculates blood to and within the heart and includes an aorta 2 (FIG.5) that supplies blood to a plurality of main coronary arteries 4 (FIG.5) (e.g., the left anterior descending (LAD) artery, the left circumflex(LCX) artery, the right coronary (RCA) artery, etc.), which may furtherdivide into branches of arteries or other types of vessels downstreamfrom the aorta 2 and the main coronary arteries 4. Thus, the exemplarymethod and system may determine various information relating to bloodflow within the aorta, the main coronary arteries, and/or other coronaryarteries or vessels downstream from the main coronary arteries. Althoughthe aorta and coronary arteries (and the branches that extend therefrom)are discussed below, the disclosed method and system may also apply toother types of vessels.

In an exemplary embodiment, the information determined by the disclosedmethods and systems may include, but is not limited to, various bloodflow characteristics or parameters, such as blood flow velocity,pressure (or a ratio thereof), flow rate, and FFR at various locationsin the aorta, the main coronary arteries, and/or other coronary arteriesor vessels downstream from the main coronary arteries. This informationmay be used to determine whether a lesion is functionally significantand/or whether to treat the lesion. This information may be determinedusing information obtained noninvasively from the patient. As a result,the decision whether to treat a lesion may be made without the cost andrisk associated with invasive procedures.

FIG. 1 shows aspects of a system for providing various informationrelating to coronary blood flow in a specific patient, according to anexemplary embodiment. A three-dimensional model 10 of the patient'sanatomy may be created using data obtained noninvasively from thepatient as will be described below in more detail. Otherpatient-specific information may also be obtained noninvasively. In anexemplary embodiment, the portion of the patient's anatomy that isrepresented by the three-dimensional model 10 may include at least aportion of the aorta and a proximal portion of the main coronaryarteries (and the branches extending or emanating therefrom) connectedto the aorta.

Various physiological laws or relationships 20 relating to coronaryblood flow may be deduced, e.g., from experimental data as will bedescribed below in more detail. Using the three-dimensional anatomicalmodel 10 and the deduced physiological laws 20, a plurality of equations30 relating to coronary blood flow may be determined as will bedescribed below in more detail. For example, the equations 30 may bedetermined and solved using any numerical method, e.g., finitedifference, finite volume, spectral, lattice Boltzmann, particle-based,level set, finite element methods, etc. The equations 30 may be solvableto determine information (e.g., pressure, velocity, FFR, etc.) about thecoronary blood flow in the patient's anatomy at various points in theanatomy represented by the model 10.

The equations 30 may be solved using a computer 40. Based on the solvedequations, the computer 40 may output one or more images or simulationsindicating information relating to the blood flow in the patient'sanatomy represented by the model 10. For example, the image(s) mayinclude a simulated blood pressure model 50, a simulated blood flow orvelocity model 52, a computed FFR (cFFR) model 54, etc., as will bedescribed in further detail below. The simulated blood pressure model50, the simulated blood flow model 52, and the cFFR model 54 provideinformation regarding the respective pressure, velocity, and cFFR atvarious locations along three dimensions in the patient's anatomyrepresented by the model 10. cFFR may be calculated as the ratio of theblood pressure at a particular location in the model 10 divided by theblood pressure in the aorta, e.g., at the inflow boundary of the model10, under conditions of increased coronary blood flow, e.g.,conventionally induced by intravenous administration of adenosine.

In an exemplary embodiment, the computer 40 may include one or morenon-transitory computer-readable storage devices that store instructionsthat, when executed by a processor, computer system, etc., may performany of the actions described herein for providing various informationrelating to blood flow in the patient. The computer 40 may include adesktop or portable computer, a workstation, a server, a personaldigital assistant, or any other computer system. The computer 40 mayinclude a processor, a read-only memory (ROM), a random access memory(RAM), an input/output (I/O) adapter for connecting peripheral devices(e.g., an input device, output device, storage device, etc.), a userinterface adapter for connecting input devices such as a keyboard, amouse, a touch screen, a voice input, and/or other devices, acommunications adapter for connecting the computer 40 to a network, adisplay adapter for connecting the computer 40 to a display, etc. Forexample, the display may be used to display the three-dimensional model10 and/or any images generated by solving the equations 30, such as thesimulated blood pressure model 50, the simulated blood flow model 52,and/or the cFFR model 54.

FIG. 2 shows aspects of a method for providing various informationrelating to blood flow in a specific patient, according to anotherexemplary embodiment. The method may include obtaining patient-specificanatomical data, such as information regarding the patient's anatomy(e.g., at least a portion of the aorta and a proximal portion of themain coronary arteries (and the branches extending therefrom) connectedto the aorta), and preprocessing the data (step 100). Thepatient-specific anatomical data may be obtained noninvasively, e.g., byCCTA, as will be described below.

A three-dimensional model of the patient's anatomy may be created basedon the obtained anatomical data (step 200). For example, thethree-dimensional model may be the three-dimensional model 10 of thepatient's anatomy described above in connection with FIG. 1.

The three-dimensional model may be prepared for analysis and boundaryconditions may be determined (step 300). For example, thethree-dimensional model 10 of the patient's anatomy described above inconnection with FIG. 1 may be trimmed and discretized into a volumetricmesh, e.g., a finite element or finite volume mesh. The volumetric meshmay be used to generate the equations 30 described above in connectionwith FIG. 1.

Boundary conditions may also be assigned and incorporated into theequations 30 described above in connection with FIG. 1. The boundaryconditions provide information about the three-dimensional model 10 atits boundaries, e.g., the inflow boundaries 322 (FIG. 8), the outflowboundaries 324 (FIG. 8), the vessel wall boundaries 326 (FIG. 8), etc.The inflow boundaries 322 may include the boundaries through which flowis directed into the anatomy of the three-dimensional model, such as atan end of the aorta near the aortic root (e.g., end A shown in FIG. 16).Each inflow boundary 322 may be assigned, e.g., with a prescribed valueor field for velocity, flow rate, pressure, or other characteristic, bycoupling a heart model and/or a lumped parameter model to the boundary,etc. The outflow boundaries 324 may include the boundaries through whichflow is directed outward from the anatomy of the three-dimensionalmodel, such as at an end of the aorta near the aortic arch (e.g., end Bshown in FIG. 16), and the downstream ends of the main coronary arteriesand the branches that extend therefrom (e.g., ends a-m shown in FIG.16). Each outflow boundary can be assigned, e.g., by coupling a lumpedparameter or distributed (e.g., a one-dimensional wave propagation)model, as will be described in detail below. The prescribed values forthe inflow and/or outflow boundary conditions may be determined bynoninvasively measuring physiologic characteristics of the patient, suchas, but not limited to, cardiac output (the volume of blood flow fromthe heart), blood pressure, myocardial mass, etc. The vessel wallboundaries may include the physical boundaries of the aorta, the maincoronary arteries, and/or other coronary arteries or vessels of thethree-dimensional model 10.

The computational analysis may be performed using the preparedthree-dimensional model and the determined boundary conditions (step400) to determine blood flow information for the patient. For example,the computational analysis may be performed with the equations 30 andusing the computer 40 described above in connection with FIG. 1 toproduce the images described above in connection with FIG. 1, such asthe simulated blood pressure model 50, the simulated blood flow model52, and/or the cFFR model 54.

The method may also include providing patient-specific treatment optionsusing the results (step 500). For example, the three-dimensional model10 created in step 200 and/or the boundary conditions assigned in step300 may be adjusted to model one or more treatments, e.g., placing acoronary stent in one of the coronary arteries represented in thethree-dimensional model 10 or other treatment options. Then, thecomputational analysis may be performed as described above in step 400in order to produce new images, such as updated versions of the bloodpressure model 50, the blood flow model 52, and/or the cFFR model 54.These new images may be used to determine a change in blood flowvelocity and pressure if the treatment option(s) are adopted.

The systems and methods disclosed herein may be incorporated into asoftware tool accessed by physicians to provide a noninvasive means toquantify blood flow in the coronary arteries and to assess thefunctional significance of coronary artery disease. In addition,physicians may use the software tool to predict the effect of medical,interventional, and/or surgical treatments on coronary artery bloodflow. The software tool may prevent, diagnose, manage, and/or treatdisease in other portions of the cardiovascular system includingarteries of the neck (e.g., carotid arteries), arteries in the head(e.g., cerebral arteries), arteries in the thorax, arteries in theabdomen (e.g., the abdominal aorta and its branches), arteries in thearms, or arteries in the legs (e.g., the femoral and poplitealarteries). The software tool may be interactive to enable physicians todevelop optimal personalized therapies for patients.

For example, the software tool may be incorporated at least partiallyinto a computer system, e.g., the computer 40 shown in FIG. 1 used by aphysician or other user. The computer system may receive data obtainednoninvasively from the patient (e.g., data used to create thethree-dimensional model 10, data used to apply boundary conditions orperform the computational analysis, etc.). For example, the data may beinput by the physician or may be received from another source capable ofaccessing and providing such data, such as a radiology or other medicallab. The data may be transmitted via a network or other system forcommunicating the data, or directly into the computer system. Thesoftware tool may use the data to produce and display thethree-dimensional model 10 or other models/meshes and/or any simulationsor other results determined by solving the equations 30 described abovein connection with FIG. 1, such as the simulated blood pressure model50, the simulated blood flow model 52, and/or the cFFR model 54. Thus,the software tool may perform steps 100-500. In step 500, the physicianmay provide further inputs to the computer system to select possibletreatment options, and the computer system may display to the physiciannew simulations based on the selected possible treatment options.Further, each of steps 100-500 shown in FIG. 2 may be performed usingseparate software packages or modules.

Alternatively, the software tool may be provided as part of a web-basedservice or other service, e.g., a service provided by an entity that isseparate from the physician. The service provider may, for example,operate the web-based service and may provide a web portal or otherweb-based application (e.g., run on a server or other computer systemoperated by the service provider) that is accessible to physicians orother users via a network or other methods of communicating data betweencomputer systems. For example, the data obtained noninvasively from thepatient may be provided to the service provider, and the serviceprovider may use the data to produce the three-dimensional model 10 orother models/meshes and/or any simulations or other results determinedby solving the equations 30 described above in connection with FIG. 1,such as the simulated blood pressure model 50, the simulated blood flowmodel 52, and/or the cFFR model 54. Then, the web-based service maytransmit information relating to the three-dimensional model 10 or othermodels/meshes and/or the simulations so that the three-dimensional model10 and/or the simulations may be displayed to the physician on thephysician's computer system. Thus, the web-based service may performsteps 100-500 and any other steps described below for providingpatient-specific information. In step 500, the physician may providefurther inputs, e.g., to select possible treatment options or make otheradjustments to the computational analysis, and the inputs may betransmitted to the computer system operated by the service provider(e.g., via the web portal). The web-based service may produce newsimulations or other results based on the selected possible treatmentoptions, and may communicate information relating to the new simulationsback to the physician so that the new simulations may be displayed tothe physician.

It is to be understood that one or more of the steps described hereinmay be performed by one or more human operators (e.g., a cardiologist orother physician, the patient, an employee of the service providerproviding the web-based service or other service provided by a thirdparty, other user, etc.), or one or more computer systems used by suchhuman operator(s), such as a desktop or portable computer, aworkstation, a server, a personal digital assistant, etc. The computersystem(s) may be connected via a network or other method ofcommunicating data.

FIG. 3 shows further aspects of the exemplary method for providingvarious information relating to blood flow in a specific patient. Theaspects shown in FIG. 3 may be incorporated into the software tool thatmay be incorporated at least partially into a computer system and/or aspart of a web-based service.

II. Obtaining and Preprocessing Patient-Specific Anatomical Data

As described above in connection with step 100 shown in FIG. 2, theexemplary method may include obtaining patient-specific anatomical data,such as information regarding the patient's heart, and preprocessing thedata. In an exemplary embodiment, step 100 may include the followingsteps.

Initially, a patient may be selected. For example, the patient may beselected by the physician when the physician determines that informationabout the patient's coronary blood flow is desired, e.g., if the patientis experiencing symptoms associated with coronary artery disease, suchas chest pain, heart attack, etc.

Patient-specific anatomical data may be obtained, such as data regardingthe geometry of the patient's heart, e.g., at least a portion of thepatient's aorta, a proximal portion of the main coronary arteries (andthe branches extending therefrom) connected to the aorta, and themyocardium. The patient-specific anatomical data may be obtainednoninvasively, e.g., using a noninvasive imaging method. For example,CCTA is an imaging method in which a user may operate a computertomography (CT) scanner to view and create images of structures, e.g.,the myocardium, the aorta, the main coronary arteries, and other bloodvessels connected thereto. The CCTA data may be time-varying, e.g., toshow changes in vessel shape over a cardiac cycle. CCTA may be used toproduce an image of the patient's heart. For example, 64-slice CCTA datamay be obtained, e.g., data relating to 64 slices of the patient'sheart, and assembled into a three-dimensional image. FIG. 4 shows anexample of a three-dimensional image 120 produced by the 64-slice CCTAdata.

Alternatively, other noninvasive imaging methods, such as magneticresonance imaging (MRI) or ultrasound (US), or invasive imaging methods,such as digital subtraction angiography (DSA), may be used to produceimages of the structures of the patient's anatomy. The imaging methodsmay involve injecting the patient intravenously with a contrast agent toenable identification of the structures of the anatomy. The resultingimaging data (e.g., provided by CCTA, MRI, etc.) may be provided by athird-party vendor, such as a radiology lab or a cardiologist, by thepatient's physician, etc.

Other patient-specific anatomical data may also be determined from thepatient noninvasively. For example, physiological data such as thepatient's blood pressure, baseline heart rate, height, weight,hematocrit, stroke volume, etc., may be measured. The blood pressure maybe the blood pressure in the patient's brachial artery (e.g., using apressure cuff), such as the maximum (systolic) and minimum (diastolic)pressures.

The patient-specific anatomical data obtained as described above may betransferred over a secure communication line (e.g., via a network). Forexample, the data may be transferred to a server or other computersystem for performing the computational analysis, e.g., thecomputational analysis described above in step 400. In an exemplaryembodiment, the data may be transferred to a server or other computersystem operated by a service provider providing a web-based service.Alternatively, the data may be transferred to a computer system operatedby the patient's physician or other user.

Referring back to FIG. 3, the transferred data may be reviewed todetermine if the data is acceptable (step 102). The determination may beperformed by the user and/or by the computer system. For example, thetransferred data (e.g., the CCTA data and other data) may be verified bya user and/or by the computer system, e.g., to determine if the CCTAdata is complete (e.g., includes sufficient portions of the aorta andthe main coronary arteries) and corresponds to the correct patient.

The transferred data (e.g., the CCTA data and other data) may also bepreprocessed and assessed. The preprocessing and/or assessment may beperformed by a user and/or by the computer system and may include, e.g.,checking for misregistration, inconsistencies, or blurring in the CCTAdata, checking for stents shown in the CCTA data, checking for otherartifacts that may prevent the visibility of lumens of the bloodvessels, checking for sufficient contrast between the structures (e.g.,the aorta, the main coronary arteries, and other blood vessels) and theother portions of the patient, etc.

The transferred data may be evaluated to determine if the data isacceptable based on the verification, preprocessing, and/or assessmentdescribed above. During the verification, preprocessing, and/orassessment described above, the user and/or computer system may be ableto correct certain errors or problems with the data. If, however, thereare too many errors or problems, then the data may be determined to beunacceptable, and the user and/or computer system may generate arejection report explaining the errors or problems necessitating therejection of the transferred data. Optionally, a new CCTA scan may beperformed and/or the physiological data described above may be measuredfrom the patient again. If the transferred data is determined to beacceptable, then the method may proceed to step 202 described below.

Accordingly, step 102 shown in FIG. 3 and described above may beconsidered as a substep of step 100 of FIG. 2.

III. Creating The Three-Dimensional Model Based On Obtained AnatomicalData

As described above in connection with step 200 shown in FIG. 2, theexemplary method may include creating the three-dimensional model basedon the obtained anatomical data. In an exemplary embodiment, step 200may include the following steps.

Using the CCTA data, a three-dimensional model of the coronary vesselsmay be generated. FIG. 5 shows an example of the surface of athree-dimensional model 220 generated using the CCTA data. For example,the model 220 may include, e.g., at least a portion of the aorta, atleast a proximal portion of one or more main coronary arteries connectedto that portion of the aorta, at least a proximal portion of one or morebranches connected to the main coronary arteries, etc. The modeledportions of the aorta, the main coronary arteries, and/or the branchesmay be interconnected and treelike such that no portion is disconnectedfrom the rest of the model 220. The process of forming the model 220 iscalled segmentation.

Referring back to FIG. 3, the computer system may automatically segmentat least a portion of the aorta (step 202) and the myocardium (or otherheart tissue, or other tissue connected to the arteries to be modeled)(step 204). The computer system may also segment at least a portion ofthe main coronary arteries connected to the aorta. In an exemplaryembodiment, the computer system may allow the user to select one or morecoronary artery root or starting points (step 206) in order to segmentthe main coronary arteries.

Segmentation may be performed using various methods. Segmentation may beperformed automatically by the computer system based on user inputs orwithout user inputs. For example, in an exemplary embodiment, the usermay provide inputs to the computer system in order to generate a firstinitial model. For example, the computer system may display to the userthe three-dimensional image 120 (FIG. 4) or slices thereof produced fromthe CCTA data. The three-dimensional image 120 may include portions ofvarying intensity of lightness. For example, lighter areas may indicatethe lumens of the aorta, the main coronary arteries, and/or thebranches. Darker areas may indicate the myocardium and other tissue ofthe patient's heart.

FIG. 6 shows a portion of a slice 222 of the three-dimensional image 120that may be displayed to the user, and the slice 222 may include an area224 of relative lightness. The computer system may allow the user toselect the area 224 of relative lightness by adding one or more seeds226, and the seeds 226 may serve as coronary artery root or startingpoints for segmenting the main coronary arteries. At the command of theuser, the computer system may then use the seeds 226 as starting pointsto form the first initial model. The user may add seeds 226 in one ormore of the aorta and/or the individual main coronary arteries.Optionally, the user may also add seeds 226 in one or more of thebranches connected to the main coronary arteries. Alternatively, thecomputer system may place the seeds automatically, e.g., using extractedcenterline information. The computer system may determine an intensityvalue of the image 120 where the seeds 226 have been placed and may formthe first initial model by expanding the seeds 226 along the portions ofthe image 120 having the same intensity value (or within a range orthreshold of intensity values centered at the selected intensity value).Thus, this method of segmentation may be called “threshold-basedsegmentation.”

FIG. 7 shows a portion 230 of the first initial model that is formed byexpanding the seeds 226 of FIG. 6. Accordingly, the user inputs theseeds 226 as starting points for the computer system to begin formingthe first initial model. This process may be repeated until the entireportions of interest, e.g., the portions of the aorta and/or the maincoronary arteries, are segmented. Alternatively, the first initial modelmay be generated by the computer system without user inputs.

Alternatively, segmentation may be performed using a method called“edge-based segmentation.” In an exemplary embodiment, both thethreshold-based and edge-based segmentation methods may be performed, aswill be described below, to form the model 220.

A second initial model may be formed using the edge-based segmentationmethod. With this method, the lumen edges of the aorta and/or the maincoronary arteries may be located. For example, in an exemplaryembodiment, the user may provide inputs to the computer system, e.g.,the seeds 226 as described above, in order to generate the secondinitial model. The computer system may expand the seeds 226 along theportions of the image 120 until the edges are reached. The lumen edgesmay be located, e.g., by the user visually, and/or by the computersystem (e.g., at locations where there is a change in intensity valueabove a set threshold). The edge-based segmentation method may beperformed by the computer system and/or the user.

The myocardium or other tissue may also be segmented based on the CCTAdata in step 204. For example, the CCTA data may be analyzed todetermine the location of the internal and external surfaces of themyocardium, e.g., the left and/or right ventricles. The locations of thesurfaces may be determined based on the contrast (e.g., relativedarkness and lightness) of the myocardium compared to other structuresof the heart in the CCTA data. Thus, the geometry of the myocardium maybe determined.

The segmentation of the aorta, the myocardium, and/or the main coronaryarteries may be reviewed and/or corrected, if necessary (step 208). Thereview and/or correction may be performed by the computer system and/orthe user. For example, in an exemplary embodiment, the computer systemmay automatically review the segmentation, and the user may manuallycorrect the segmentation if there are any errors, e.g., if any portionsof the aorta, the myocardium, and/or the main coronary arteries in themodel 220 are missing or inaccurate.

For example, the first and second initial models described above may becompared to ensure that the segmentation of the aorta and/or the maincoronary arteries is accurate. Any areas of discrepancy between thefirst and second initial models may be compared to correct thesegmentation and to form the model 220. For example, the model 220 maybe an average between the first and second initial models.Alternatively, only one of the segmentation methods described above maybe performed, and the initial model formed by that method may be used asthe model 220.

The myocardial mass may be calculated (step 240). The calculation may beperformed by the computer system. For example, the myocardial volume maybe calculated based on the locations of the surfaces of the myocardiumdetermined as described above, and the calculated myocardial volume maybe multiplied by the density of the myocardium to calculate themyocardial mass. The density of the myocardium may be preset.

The centerlines of the various vessels (e.g., the aorta, the maincoronary arteries, etc.) of the model 220 (FIG. 5) may be determined(step 242). In an exemplary embodiment, the determination may beperformed automatically by the computer system.

The centerlines determined in step 242 may be reviewed and/or corrected,if necessary (step 244). The review and/or correction may be performedby the computer system and/or the user. For example, in an exemplaryembodiment, the computer system may automatically review thecenterlines, and the user may manually correct the centerlines if thereare any errors, e.g., if any centerlines are missing or inaccurate.

Calcium or plaque (causing narrowing of a vessel) may be detected (step246). In an exemplary embodiment, the computer system may automaticallydetect the plaque. For example, the plaque may be detected in thethree-dimensional image 120 and removed from the model 220. The plaquemay be identified in the three-dimensional image 120 since the plaqueappears as areas that are even lighter than the lumens of the aorta, themain coronary arteries, and/or the branches. Thus, the plaque may bedetected by the computer system as having an intensity value below a setvalue or may be detected visually by the user. After detecting theplaque, the computer system may remove the plaque from the model 220 sothat the plaque is not considered as part of the lumen or open space inthe vessels. Alternatively, the computer system may indicate the plaqueon the model 220 using a different color, shading, or other visualindicator than the aorta, the main coronary arteries, and/or thebranches.

The computer system may also automatically segment the detected plaque(step 248). For example, the plaque may be segmented based on the CCTAdata. The CCTA data may be analyzed to locate the plaque (or a surfacethereof) based on the contrast (e.g., relative darkness and lightness)of the plaque compared to other structures of the heart in the CCTAdata. Thus, the geometry of the plaque may also be determined.

The segmentation of the plaque may be reviewed and/or corrected, ifnecessary (step 250). The review and/or correction may be performed bythe computer system and/or the user. For example, in an exemplaryembodiment, the computer system may automatically review thesegmentation, and the user may manually correct the segmentation ifthere are any errors, e.g., if any plaque is missing or showninaccurately.

The computer system may automatically segment the branches connected tothe main coronary arteries (step 252). For example, the branches may besegmented using similar methods for segmenting the main coronaryarteries, e.g., as shown in FIGS. 6 and 7 and described above inconnection with step 206. The computer system may also automaticallysegment the plaque in the segmented branches using similar methods asdescribed above in connection with steps 248 and 250. Alternatively, thebranches (and any plaque contained therein) may be segmented at the sametime as the main coronary arteries (e.g., in step 206).

The segmentation of the branches may be reviewed and/or corrected, ifnecessary (step 254). The review and/or correction may be performed bythe computer system and/or the user. For example, in an exemplaryembodiment, the computer system may automatically review thesegmentation, and the user may manually correct the segmentation ifthere are any errors, e.g., if any portions of the branches in the model220 are missing or inaccurate.

The model 220 may be corrected if any misregistration, stents, or otherartifacts are located (e.g., during the review of the CCTA data in step102) (step 256). The correction may be performed by a user and/or by thecomputer system. For example, if a misregistration or other artifact(e.g., inconsistency, blurring, an artifact affecting lumen visibility,etc.) is located, the model 220 may be reviewed and/or corrected toavoid an artificial or false change in the cross-sectional area of avessel (e.g., an artificial narrowing). If a stent is located, the model220 may be reviewed and/or corrected to indicate the location of thestent and/or to correct the cross-sectional area of the vessel where thestent is located, e.g., based on the size of the stent.

The segmentation of the model 220 may also be independently reviewed(step 258). The review may be performed by a user and/or by the computersystem. For example, the user and/or computer system may be able toidentify certain errors with the model 220, such as correctable errorsand/or errors that may require the model 220 to be at least partiallyredone or resegmented. If such errors are identified, then thesegmentation may be determined to be unacceptable, and certain steps,e.g., one or more of steps 202-208, 240-256, depending on the error(s),may be repeated.

If the segmentation of the model 220 is independently verified asacceptable, then, optionally, the model 220 may be output and smoothed(step 260). The smoothing may be performed by the user and/or by thecomputer system. For example, ridges, points, or other discontinuousportions may be smoothed. The model 220 may be output to a separatesoftware module to be prepared for computational analysis, etc.

Accordingly, steps 202-208 and 240-260 shown in FIG. 3 and describedabove may be considered as substeps of step 200 of FIG. 2.

IV. Preparing The Model For Analysis and Determining Boundary Conditions

As described above in connection with step 300 shown in FIG. 2, theexemplary method may include preparing the model for analysis anddetermining boundary conditions. In an exemplary embodiment, step 300may include the following steps.

A. Preparing the Model For Analysis

Referring back to FIG. 3, the cross-sectional areas of the variousvessels (e.g., the aorta, the main coronary arteries, and/or thebranches) of the model 220 (FIG. 5) may also be determined (step 304).In an exemplary embodiment, the determination may be performed by thecomputer system.

The model 220 (FIG. 5) may be trimmed (step 306) and a solid model maybe generated. FIG. 8 shows an example of the trimmed solid model 320prepared based on a model similar to the model 220 shown in FIG. 5. Thesolid model 320 is a three-dimensional patient-specific geometric model.In an exemplary embodiment, the trimming may be performed by thecomputer system, with or without a user's input. Each of the inflowboundaries 322 and outflow boundaries 324 may be trimmed such that thesurface forming the respective boundary is perpendicular to thecenterlines determined in step 242. The inflow boundaries 322 mayinclude the boundaries through which flow is directed into the anatomyof the model 320, such as at an upstream end of the aorta, as shown inFIG. 8. The outflow boundaries 324 may include the boundaries throughwhich flow is directed outward from the anatomy of the model 320, suchas at a downstream end of the aorta and the downstream ends of the maincoronary arteries and/or branches.

B. Determining Boundary Conditions

Boundary conditions may be provided to describe what is occurring at theboundaries of the model, e.g., the three-dimensional solid model 320 ofFIG. 8. For example, the boundary conditions may relate to at least oneblood flow characteristic associated with the patient's modeled anatomy,e.g., at the boundaries of the modeled anatomy, and the blood flowcharacteristic(s) may include blood flow velocity, pressure, flow rate,FFR, etc. By appropriately determining the boundary conditions, acomputational analysis may be performed to determine information atvarious locations within the model. Examples of boundary conditions andmethods for determining such boundary conditions will now be described.

In an exemplary embodiment, the determined boundary conditions maysimplify the structures upstream and downstream from the portions of thevessels represented by the solid model 320 into a one- ortwo-dimensional reduced order model. An exemplary set of equations andother details for determining the boundary conditions are disclosed, forexample, in U.S. Patent Application Publication No. 2010/0241404 andU.S. Provisional Application No. 61/210,401, which are both entitled“Patient-Specific Hemodynamics of the Cardiovascular System” and herebyincorporated by reference in their entirety.

Boundary conditions may vary depending on the physiological condition ofthe patient since blood flow though the heart may differ depending onthe physiological condition of the patient. For example, FFR istypically measured under the physiological condition of hyperemia, whichgenerally occurs when the patient is experiencing increased blood flowin the heart, e.g., due to stress, etc. The FFR is the ratio of thecoronary pressure to aortic pressure under conditions of maximum stress.Hyperemia may also be induced pharmacologically, e.g., with adenosine.FIGS. 9-11 show examples of a calculated FFR (cFFR) model that indicatesthe change in the ratio of coronary pressure to aortic pressure in themodel 320, depending on the physiological condition of the patient (atrest, under maximum hyperemia, or under maximum exercise). FIG. 9 showsminimal variation in the ratio of coronary pressure to aortic pressurethroughout the model 320 when the patient is at rest. FIG. 10 showsgreater variation in the ratio of coronary pressure to aortic pressurethroughout the model 320 when the patient is undergoing maximumhyperemia. FIG. 11 shows even greater variation in the ratio of coronarypressure to aortic pressure throughout the model 320 when the patient isundergoing maximum exercise.

Referring back to FIG. 3, boundary conditions for hyperemia conditionsmay be determined (step 310). In an exemplary embodiment, the effect ofadenosine may be modeled using a decrease in coronary artery resistanceby a factor of 1-5 fold, a decrease in aortic blood pressure ofapproximately 0-20%, and an increase in heart rate of approximately0-20%. For example, the effect of adenosine may be modeled using adecrease in coronary artery resistance by a factor of 4 fold, a decreasein aortic blood pressure of approximately 10%, and an increase in heartrate of approximately 10%. Although the boundary conditions forhyperemia conditions are determined in the exemplary embodiment, it isunderstood that boundary conditions for other physiological states, suchas rest, varying degrees of hyperemia, varying degrees of exercise,exertion, stress, or other conditions, may be determined.

Boundary conditions provide information about the three-dimensionalsolid model 320 at its boundaries, e.g., the inflow boundaries 322, theoutflow boundaries 324, vessel wall boundaries 326, etc., as shown inFIG. 8. The vessel wall boundaries 326 may include the physicalboundaries of the aorta, the main coronary arteries, and/or othercoronary arteries or vessels of the model 320.

Each inflow or outflow boundary 322, 324 may be assigned a prescribedvalue or field of values for velocity, flow rate, pressure, or otherblood flow characteristic. Alternatively, each inflow or outflowboundary 322, 324 may be assigned by coupling a heart model to theboundary, a lumped parameter or distributed (e.g. one-dimensional wavepropagation) model, another type of one- or two-dimensional model, orother type of model. The specific boundary conditions may be determinedbased on, e.g., the geometry of the inflow or outflow boundaries 322,324 determined from the obtained patient-specific information, or othermeasured parameters, such as cardiac output, blood pressure, themyocardial mass calculated in step 240, etc.

i. Determining Reduced Order Models

The upstream and downstream structures connected to the solid model 320may be represented as reduced order models representing the upstream anddownstream structures. For example, FIGS. 12-15 show aspects of a methodfor preparing a lumped parameter model from three-dimensionalpatient-specific anatomical data at one of the outflow boundaries 324,according to an exemplary embodiment. The method may be performedseparately from and prior to the methods shown in FIGS. 2 and 3.

FIG. 12 shows a portion 330 of the solid model 320 of one of the maincoronary arteries or the branches extending therefrom, and FIG. 13 showsthe portion of the centerlines determined in step 242 of the portion 330shown in FIG. 12.

The portion 330 may be divided into segments 332. FIG. 14 shows anexample of the segments 332 that may be formed from the portion 330. Theselection of the lengths of the segments 332 may be performed by theuser and/or the computer system. The segments 332 may vary in length,depending, for example, on the geometry of the segments 332. Varioustechniques may be used to segment the portion 330. For example, diseasedportions, e.g., portions with a relatively narrow cross-section, alesion, and/or a stenosis (an abnormal narrowing in a blood vessel), maybe provided in one or more separate segments 332. The diseased portionsand stenoses may be identified, e.g., by measuring the cross-sectionalarea along the length of the centerline and calculating locally minimumcross-sectional areas.

The segments 332 may be approximated by a circuit diagram including oneor more (linear or nonlinear) resistors 334 and/or other circuitelements (e.g., capacitors, inductors, etc.). FIG. 15 shows an exampleof the segments 332 replaced by a series of linear and nonlinearresistors 334. The individual resistances of the resistors 334 may bedetermined, e.g., based on an estimated flow and/or pressure across thecorresponding segment 332.

The resistance may be constant, linear, or non-linear, e.g., dependingon the estimated flow rate through the corresponding segment 332. Formore complex geometries, such as a stenosis, the resistance may varywith flow rate. Resistances for various geometries may be determinedbased on a computational analysis (e.g., a finite difference, finitevolume, spectral, lattice Boltzmann, particle-based, level set,isogeometric, or finite element method, or other computational fluiddynamics (CFD) analytical technique), and multiple solutions from thecomputational analysis performed under different flow and pressureconditions may be used to derive patient-specific, vessel-specific,and/or lesion-specific resistances. The results may be used to determineresistances for various types of features and geometries of any segmentthat may be modeled. As a result, deriving patient-specific,vessel-specific, and/or lesion-specific resistances as described abovemay allow the computer system to recognize and evaluate more complexgeometry such as asymmetric stenosis, multiple lesions, lesions atbifurcations and branches and tortuous vessels, etc.

Capacitors may be also included, and capacitance may be determined,e.g., based on elasticity of the vessel walls of the correspondingsegment. Inductors may be included, and inductance may be determined,e.g., based on inertial effects related to acceleration or decelerationof the blood volume flowing through the corresponding segment.

The individual values for resistance, capacitance, inductance, and othervariables associated with other electrical components used in the lumpedparameter model may be derived based on data from many patients, andsimilar vessel geometries may have similar values. Thus, empiricalmodels may be developed from a large population of patient-specificdata, creating a library of values corresponding to specific geometricfeatures that may be applied to similar patients in future analyses.Geometries may be matched between two different vessel segments toautomatically select the values for a segment 332 of a patient from aprevious simulation.

ii. Exemplary Lumped Parameter Models

Alternatively, instead of performing the steps described above inconnection with FIGS. 12-15, the lumped parameter models may be preset.For example, FIG. 16 shows examples of lumped parameter models 340, 350,360 representing the upstream and downstream structures at the inflowand outflow boundaries 322, 324 of the solid model 320. End A is locatedat the inflow boundary 322, and ends a-m and B are located at theoutflow boundaries.

A lumped parameter heart model 340 may be used to determine the boundarycondition at the end A at the inflow boundary 322 of the solid model320. The lumped parameter heart model 340 may be used to represent bloodflow from the heart under hyperemia conditions. The lumped parameterheart model 340 includes various parameters (e.g., P_(LA), R_(AV),L_(AV), R_(V-Art), L_(V-Art), and E(t)) that may be determined based onknown information regarding the patient, e.g., an aortic pressure, thepatient's systolic and diastolic blood pressures (e.g., as determined instep 100), the patient's cardiac output (the volume of blood flow fromthe heart, e.g., calculated based on the patient's stroke volume andheart rate determined in step 100), and/or constants determinedexperimentally.

A lumped parameter coronary model 350 may be used to determine theboundary conditions at the ends a-m at the outflow boundaries 324 of thesolid model 320 located at the downstream ends of the main coronaryarteries and/or the branches that extend therefrom. The lumped parametercoronary model 350 may be used to represent blood flow exiting from themodeled vessels through the ends a-m under hyperemia conditions. Thelumped parameter coronary model 350 includes various parameters (e.g.,R_(a), C_(a), R_(a-micro), C_(im), and R_(v)) that may be determinedbased on known information regarding the patient, e.g., the calculatedmyocardial mass (e.g., as determined in step 240) and terminal impedanceat the ends a-m (e.g., determined based on the cross-sectional areas ofthe vessels at the ends a-m as determined in step 304).

For example, the calculated myocardial mass may be used to estimate abaseline (resting) mean coronary flow through the plurality of outflowboundaries 324. This relationship may be based on anexperimentally-derived physiological law (e.g., of the physiologicallaws 20 of FIG. 1) that correlates the mean coronary flow Q with themyocardial mass M (e.g., as determined in step 240) as Q∝Q_(o)M^(α),where α is a preset scaling exponent and Q_(o) is a preset constant. Thetotal coronary flow Q at the outflow boundaries 324 under baseline(resting) conditions and the patient's blood pressure (e.g., asdetermined in step 100) may then be used to determine a total resistanceRat the outflow boundaries 324 based on a preset, experimentally-derivedequation.

The total resistance R may be distributed among the ends a-m based onthe respective cross-sectional areas of the ends a-m (e.g., asdetermined in step 304). This relationship may be based on anexperimentally-derived physiological law (e.g., of the physiologicallaws 20 of FIG. 1) that correlates the respective resistance at the endsa-m as R_(i)∝R_(i,o)d_(i) ^(β) where R_(i) is the resistance to flow atthe i-th outlet, and R_(i,o) is a preset constant, d_(i) is the diameterof that outlet, and β is a preset power law exponent, e.g., between −3and −2, −2.7 for coronary flow, −2.9 for cerebral flow, etc. Thecoronary flow through the individual ends a-m and the mean pressures atthe individual ends a-m (e.g., determined based on the individualcross-sectional areas of the ends a-m of the vessels as determined instep 304) may be used to determine a sum of the resistances of thelumped parameter coronary model 350 at the corresponding ends a-m (e.g.,R_(a)+R_(a-micro)+R_(V)). Other parameters (e.g., R_(a)/R_(a-micro),C_(a), C_(im)) may be constants determined experimentally.

A Windkessel model 360 may be used to determine the boundary conditionat the end B at the outflow boundary 324 of the solid model 320 locatedat the downstream end of the aorta toward the aortic arch. TheWindkessel model 360 may be used to represent blood flow exiting fromthe modeled aorta through the end B under hyperemia conditions. TheWindkessel model 360 includes various parameters (e.g., R_(p), R_(d),and C) that may be determined based on known information regarding thepatient, e.g., the patient's cardiac output described above inconnection with the lumped parameter heart model 340, the baseline meancoronary flow described above in connection with the lumped parametercoronary model 350, an aortic pressure (e.g., determined based on thecross-sectional area of the aorta at the end B as determined in step304), and/or constants determined experimentally.

The boundary conditions, e.g., the lumped parameter models 340, 350, 360(or any of the constants included therein) or other reduced order model,may be adjusted based on other factors. For example, resistance valuesmay be adjusted (e.g., increased) if a patient has a lower flow tovessel size ratio due to a comparatively diminished capacity to dilatevessels under physiologic stress. Resistance values may also be adjustedif the patient has diabetes, is under medication, has undergone pastcardiac events, etc.

Alternate lumped parameter or distributed, one-dimensional networkmodels may be used to represent the coronary vessels downstream of thesolid model 320. Myocardial perfusion imaging using MRI, CT, PET, orSPECT may be used to assign parameters for such models. Also, alternateimaging sources, e.g., magnetic resonance angiography (MRA),retrospective cine gating or prospective cine gating computed tomographyangiography (CTA), etc., may be used to assign parameters for suchmodels. Retrospective cine gating may be combined with image processingmethods to obtain ventricular chamber volume changes over the cardiaccycle to assign parameters to a lumped parameter heart model.

Simplifying a portion of the patient's anatomy using the lumpedparameter models 340, 350, 360, or other reduced order one- ortwo-dimensional model allows the computational analysis (e.g., step 402of FIG. 3 described below) to be performed more quickly, particularly ifthe computational analysis is performed multiple times such as whenevaluating possible treatment options (e.g., step 500 of FIG. 2) inaddition to the untreated state (e.g., step 400 of FIGS. 2 and 3), whilemaintaining high accuracy with the final results.

In an exemplary embodiment, the determination of the boundary conditionsmay be performed by the computer system based on the user's inputs, suchas patient-specific physiological data obtained in step 100.

C. Creating the Three-Dimensional Mesh

Referring back to FIG. 3, a three-dimensional mesh may be generatedbased on the solid model 320 generated in step 306 (step 312). FIGS.17-19 show an example of a three-dimensional mesh 380 prepared based onthe solid model 320 generated in step 306. The mesh 380 includes aplurality of nodes 382 (meshpoints or gridpoints) along the surfaces ofthe solid model 320 and throughout the interior of the solid model 320.The mesh 380 may be created with tetrahedral elements (having pointsthat form the nodes 382), as shown in FIGS. 18 and 19. Alternatively,elements having other shapes may be used, e.g., hexahedrons or otherpolyhedrons, curvilinear elements, etc. In an exemplary embodiment, thenumber of nodes 382 may be in the millions, e.g., five to fifty million.The number of nodes 382 increases as the mesh 380 becomes finer. With ahigher number of nodes 382, information may be provided at more pointswithin the model 320, but the computational analysis may take longer torun since a greater number of nodes 382 increases the number ofequations (e.g., the equations 30 shown in FIG. 1) to be solved. In anexemplary embodiment, the generation of the mesh 380 may be performed bythe computer system, with or without a user's input (e.g., specifying anumber of the nodes 382, the shapes of the elements, etc.).

Referring back to FIG. 3, the mesh 380 and the determined boundaryconditions may be verified (step 314). The verification may be performedby a user and/or by the computer system. For example, the user and/orcomputer system may be able to identify certain errors with the mesh 380and/or the boundary conditions that require the mesh 380 and/or theboundary conditions to be redone, e.g., if the mesh 380 is distorted ordoes not have sufficient spatial resolution, if the boundary conditionsare not sufficient to perform the computational analysis, if theresistances determined in step 310 appear to be incorrect, etc. If so,then the mesh 380 and/or the boundary conditions may be determined to beunacceptable, and one or more of steps 304-314 may be repeated. If themesh 380 and/or the boundary conditions are determined to be acceptable,then the method may proceed to step 402 described below.

In addition, the user may check that the obtained patient-specificinformation, or other measured parameters, such as cardiac output, bloodpressures, height, weight, the myocardial mass calculated in step 240,are entered correctly and/or calculated correctly.

Accordingly, steps 304-314 shown in FIG. 3 and described above may beconsidered as substeps of step 300 of FIG. 2.

V. Performing The Computational Analysis And Outputting Results

As described above in connection with step 400 shown in FIG. 2, theexemplary method may include performing the computational analysis andoutputting results. In an exemplary embodiment, step 400 may include thefollowing steps.

A. Performing the Computational Analysis

Referring to FIG. 3, the computational analysis may be performed by thecomputer system (step 402). In an exemplary embodiment, step 402 maylast minutes to hours, depending, e.g., on the number of nodes 382 inthe mesh 380 (FIGS. 17-19), etc.

The analysis involves generating a series of equations that describe theblood flow in the model 320 from which the mesh 380 was generated. Asdescribed above, in the exemplary embodiment, the desired informationrelates to the simulation of blood flow through the model 320 underhyperemic conditions.

The analysis also involves using a numerical method to solve thethree-dimensional equations of blood flow using the computer system. Forexample, the numerical method may be a known method, such as finitedifference, finite volume, spectral, lattice Boltzmann, particle-based,level set, isogeometric, or finite element methods, or othercomputational fluid dynamics (CFD) numerical techniques.

Using these numerical methods, the blood may be modeled as a Newtonian,a non-Newtonian, or a multiphase fluid. The patient's hematocrit orother factors measured in step 100 may be used to determine bloodviscosity for incorporation in the analysis. The blood vessel walls maybe assumed to be rigid or compliant. In the latter case, equations forwall dynamics, e.g., the elastodynamics equations, may be solvedtogether with the equations for blood flow. Time-varyingthree-dimensional imaging data obtained in step 100 may be used as aninput to model changes in vessel shape over the cardiac cycle. Anexemplary set of equations and steps for performing the computationalanalysis are disclosed in further detail, for example, in U.S. Pat. No.6,236,878, which is entitled “Method for Predictive Modeling forPlanning Medical Interventions and Simulating Physiological Conditions,”and U.S. Patent Application Publication No. 2010/0241404 and U.S.Provisional Application No. 61/210,401, which are both entitled“Patient-Specific Hemodynamics of the Cardiovascular System,” all ofwhich are hereby incorporated by reference in their entirety.

The computational analysis using the prepared model and boundaryconditions may determine blood flow and pressure at each of the nodes382 of the mesh 380 representing the three-dimensional solid model 320.For example, the results of the computational analysis may includevalues for various parameters at each of the nodes 382, such as, but notlimited to, various blood flow characteristics or parameters, such asblood flow velocity, pressure, flow rate, or computed parameters, suchas cFFR, as described below. The parameters may also be interpolatedacross the three-dimensional solid model 320. As a result, the resultsof the computational analysis may provide the user with information thattypically may be determined invasively.

Referring back to FIG. 3, the results of the computational analysis maybe verified (step 404). The verification may be performed by a userand/or by the computer system. For example, the user and/or computersystem may be able to identify certain errors with the results thatrequire the mesh 380 and/or the boundary conditions to be redone orrevised, e.g., if there is insufficient information due to aninsufficient number of nodes 382, if the analysis is taking too long dueto an excessive number of nodes 382, etc.

If the results of the computational analysis are determined to beunacceptable in step 404, then the user and/or computer system maydetermine, for example, whether and how to revise or refine the solidmodel 320 generated in step 306 and/or the mesh 380 generated in step312, whether and how to revise the boundary conditions determined instep 310, or whether to make other revisions to any of the inputs forthe computational analysis. Then, one or more steps described above,e.g., steps 306-314, 402, and 404 may be repeated based on thedetermined revisions or refinements.

B. Displaying Results for Blood Pressure, Flow, and cFFR

Referring back to FIG. 3, if the results of the computational analysisare determined to be acceptable in step 404, then the computer systemmay output certain results of the computational analysis. For example,the computer system may display images generated based on the results ofthe computational analysis, such as the images described above inconnection with FIG. 1, such as the simulated blood pressure model 50,the simulated blood flow model 52, and/or the cFFR model 54. As notedabove, these images indicate the simulated blood pressure, blood flow,and cFFR under simulated hyperemia conditions, e.g., since the boundaryconditions determined in step 310 were determined with respect tohyperemia conditions.

The simulated blood pressure model 50 (FIG. 1) shows the local bloodpressure (e.g., in millimeters of mercury or mmHg) throughout thepatient's anatomy represented by the mesh 380 of FIGS. 17-19 undersimulated hyperemia conditions. The computational analysis may determinethe local blood pressure at each node 382 of the mesh 380, and thesimulated blood pressure model 50 may assign a corresponding color,shade, or other visual indicator to the respective pressures such thatthe simulated blood pressure model 50 may visually indicate thevariations in pressure throughout the model 50 without having to specifythe individual values for each node 382. For example, the simulatedblood pressure model 50 shown in FIG. 1 shows that, for this particularpatient, under simulated hyperemia conditions, the pressure may begenerally uniform and higher in the aorta (as indicated by the darkershading), and that the pressure gradually and continuously decreases asthe blood flows downstream into the main coronary arteries and into thebranches (as shown by the gradual and continuous lightening in shadingtoward the downstream ends of the branches). The simulated bloodpressure model 50 may be accompanied by a scale indicating the specificnumerical values for blood pressure, as shown in FIG. 1.

In an exemplary embodiment, the simulated blood pressure model 50 may beprovided in color, and a color spectrum may be used to indicatevariations in pressure throughout the model 50. The color spectrum mayinclude red, orange, yellow, green, blue, indigo, and violet, in orderfrom highest pressure to lowest pressure. For example, the upper limit(red) may indicate approximately 110 mmHg or more (or 80 mmHg, 90 mmHg,100 mmHg, etc.), and the lower limit (violet) may indicate approximately50 mmHg or less (or 20 mmHg, 30 mmHg, 40 mmHg, etc.), with greenindicating approximately 80 mmHg (or other value approximately halfwaybetween the upper and lower limits). Thus, the simulated blood pressuremodel 50 for some patients may show a majority or all of the aorta asred or other color towards the higher end of the spectrum, and thecolors may change gradually through the spectrum (e.g., towards thelower end of the spectrum (down to violet)) towards the distal ends ofthe coronary arteries and the branches that extend therefrom. The distalends of the coronary arteries for a particular patient may havedifferent colors, e.g., anywhere from red to violet, depending on thelocal blood pressures determined for the respective distal ends.

The simulated blood flow model 52 (FIG. 1) shows the local bloodvelocity (e.g., in centimeters per second or cm/s) throughout thepatient's anatomy represented by the mesh 380 of FIGS. 17-19 undersimulated hyperemia conditions. The computational analysis may determinethe local blood velocity at each node 382 of the mesh 380, and thesimulated blood flow model 52 may assign a corresponding color, shade,or other visual indicator to the respective velocities such that thesimulated blood flow model 52 may visually indicate the variations invelocity throughout the model 52 without having to specify theindividual values for each node 382. For example, the simulated bloodflow model 52 shown in FIG. 1 shows that, for this particular patient,under simulated hyperemia conditions, the velocity is generally higherin certain areas of the main coronary arteries and the branches (asindicated by the darker shading in area 53 in FIG. 1). The simulatedblood flow model 52 may be accompanied by a scale indicating thespecific numerical values for blood velocity, as shown in FIG. 1.

In an exemplary embodiment, the simulated blood flow model 52 may beprovided in color, and a color spectrum may be used to indicatevariations in velocity throughout the model 52. The color spectrum mayinclude red, orange, yellow, green, blue, indigo, and violet, in orderfrom highest velocity to lowest velocity. For example, the upper limit(red) may indicate approximately 100 (or 150) cm/s or more, and thelower limit (violet) may indicate approximately 0 cm/s, with greenindicating approximately 50 cm/s (or other value approximately halfwaybetween the upper and lower limits). Thus, the simulated blood flowmodel 52 for some patients may show a majority or all of the aorta as amixture of colors towards the lower end of the spectrum (e.g., greenthrough violet), and the colors may change gradually through thespectrum (e.g., towards the higher end of the spectrum (up to red)) atcertain locations where the determined blood velocities increase.

The cFFR model 54 (FIG. 1) shows the local cFFR throughout the patient'sanatomy represented by the mesh 380 of FIGS. 17-19 under simulatedhyperemia conditions. As noted above, cFFR may be calculated as theratio of the local blood pressure determined by the computationalanalysis (e.g., shown in the simulated blood pressure model 50) at aparticular node 382 divided by the blood pressure in the aorta, e.g., atthe inflow boundary 322 (FIG. 8). The computational analysis maydetermine the cFFR at each node 382 of the mesh 380, and the cFFR model54 may assign a corresponding color, shade, or other visual indicator tothe respective cFFR values such that the cFFR model 54 may visuallyindicate the variations in cFFR throughout the model 54 without havingto specify the individual values for each node 382. For example, thecFFR model 54 shown in FIG. 1 shows that, for this particular patient,under simulated hyperemia conditions, cFFR may be generally uniform andapproximately 1.0 in the aorta, and that cFFR gradually and continuouslydecreases as the blood flows downstream into the main coronary arteriesand into the branches. The cFFR model 54 may also indicate cFFR valuesat certain points throughout the cFFR model 54, as shown in FIG. 1. ThecFFR model 54 may be accompanied by a scale indicating the specificnumerical values for cFFR, as shown in FIG. 1.

In an exemplary embodiment, the cFFR model 54 may be provided in color,and a color spectrum may be used to indicate variations in pressurethroughout the model 54. The color spectrum may include red, orange,yellow, green, blue, indigo, and violet, in order from lowest cFFR(indicating functionally significant lesions) to highest cFFR. Forexample, the upper limit (violet) may indicate a cFFR of 1.0, and thelower limit (red) may indicate approximately 0.7 (or 0.75 or 0.8) orless, with green indicating approximately 0.85 (or other valueapproximately halfway between the upper and lower limits). For example,the lower limit may be determined based on a lower limit (e.g., 0.7,0.75, or 0.8) used for determining whether the cFFR measurementindicates a functionally significant lesion or other feature that mayrequire intervention. Thus, the cFFR model 54 for some patients may showa majority or all of the aorta as violet or other color towards thehigher end of the spectrum, and the colors may change gradually throughthe spectrum (e.g., towards the higher end of the spectrum (up toanywhere from red to violet) towards the distal ends of the coronaryarteries and the branches that extend therefrom. The distal ends of thecoronary arteries for a particular patient may have different colors,e.g., anywhere from red to violet, depending on the local values of cFFRdetermined for the respective distal ends.

After determining that the cFFR has dropped below the lower limit usedfor determining the presence of a functionally significant lesion orother feature that may require intervention, the artery or branch may beassessed to locate the functionally significant lesion(s). The computersystem or the user may locate the functionally significant lesion(s)based on the geometry of the artery or branch (e.g., using the cFFRmodel 54). For example, the functionally significant lesion(s) may belocated by finding a narrowing or stenosis located near (e.g., upstream)from the location of the cFFR model 54 having the local minimum cFFRvalue. The computer system may indicate or display to the user theportion(s) of the cFFR model 54 (or other model) that includes thefunctionally significant lesion(s).

Other images may also be generated based on the results of thecomputational analysis. For example, the computer system may provideadditional information regarding particular main coronary arteries,e.g., as shown in FIGS. 20-22. The coronary artery may be chosen by thecomputer system, for example, if the particular coronary artery includesthe lowest cFFR. Alternatively, the user may select the particularcoronary artery.

FIG. 20 shows a model of the patient's anatomy including results of thecomputational analysis with certain points on the model identified byindividual reference labels (e.g., LM, LAD1, LAD2, LAD3, etc.). In theexemplary embodiment shown in FIG. 21, the points are provided in theLAD artery, which is the main coronary artery having the lowest cFFR forthis particular patient, under simulated hyperemia conditions.

FIGS. 21 and 22 show graphs of certain variables over time at some orall of these points (e.g., LM, LAD1, LAD2, LAD3, etc.) and/or at certainother locations on the model (e.g., in the aorta, etc.). FIG. 21 is agraph of the pressure (e.g., in millimeters of mercury or mmHg) overtime in the aorta and at points LAD1, LAD2, and LAD3 indicated in FIG.20. The top plot on the graph indicates the pressure in the aorta, thesecond plot from the top indicates the pressure at point LAD1, the thirdplot from the top indicates the pressure at point LAD2, and the bottomplot indicates the pressure at point LAD3. FIG. 22 is a graph of theflow (e.g., in cubic centimeters per second or cc/s) over time at pointsLM, LAD1, LAD2, and LAD3 indicated in FIG. 20. In addition, other graphsmay be provided, such as a graph of shear stress over time at some orall of these points and/or at other points. The top plot on the graphindicates the flow at point LM, the second plot from the top indicatesthe flow at point LAD1, the third plot from the top indicates the flowat point LAD2, and the bottom plot indicates the flow at point LAD3.Graphs may also be provided that show the change in these variables,e.g., blood pressure, flow, velocity, or cFFR, along the length of aparticular main coronary artery and/or the branches extending therefrom.

Optionally, the various graphs and other results described above may befinalized in a report (step 406). For example, the images and otherinformation described above may be inserted into a document having a settemplate. The template may be preset and generic for multiple patients,and may be used for reporting the results of computational analyses tophysicians and/or patients. The document or report may be automaticallycompleted by the computer system after the computational analysis iscompleted.

For example, the finalized report may include the information shown inFIG. 23. FIG. 23 includes the cFFR model 54 of FIG. 1 and also includessummary information, such as the lowest cFFR values in each of the maincoronary arteries and the branches that extend therefrom. For example,FIG. 23 indicates that the lowest cFFR value in the LAD artery is 0.66,the lowest cFFR value in the LCX artery is 0.72, the lowest cFFR valuein the RCA artery is 0.80. Other summary information may include thepatient's name, the patient's age, the patient's blood pressure (BP)(e.g., obtained in step 100), the patient's heart rate (HR) (e.g.,obtained in step 100), etc. The finalized report may also includeversions of the images and other information generated as describedabove that the physician or other user may access to determine furtherinformation. The images generated by the computer system may beformatted to allow the physician or other user to position a cursor overany point to determine the value of any of the variables describedabove, e.g., blood pressure, velocity, flow, cFFR, etc., at that point.

The finalized report may be transmitted to the physician and/or thepatient. The finalized report may be transmitted using any known methodof communication, e.g., a wireless or wired network, by mail, etc.Alternatively, the physician and/or patient may be notified that thefinalized report is available for download or pick-up. Then, thephysician and/or patient may log into the web-based service to downloadthe finalized report via a secure communication line.

C. Verifying Results

Referring back to FIG. 3, the results of the computational analysis maybe independently verified (step 408). For example, the user and/orcomputer system may be able to identify certain errors with the resultsof the computational analysis, e.g., the images and other informationgenerated in step 406, that require any of the above described steps tobe redone. If such errors are identified, then the results of thecomputational analysis may be determined to be unacceptable, and certainsteps, e.g., steps 100, 200, 300, 400, substeps 102, 202-208, 240-260,304-314, and 402-408, etc., may be repeated.

Accordingly, steps 402-408 shown in FIG. 3 and described above may beconsidered as substeps of step 400 of FIG. 2.

Another method for verifying the results of the computational analysismay include measuring any of the variables included in the results,e.g., blood pressure, velocity, flow, cFFR, etc., from the patient usinganother method. In an exemplary embodiment, the variables may bemeasured (e.g., invasively) and then compared to the results determinedby the computational analysis. For example, FFR may be determined, e.g.,using a pressure wire inserted into the patient as described above, atone or more points within the patient's anatomy represented by the solidmodel 320 and the mesh 380. The measured FFR at a location may becompared with the cFFR at the same location, and the comparison may beperformed at multiple locations. Optionally, the computational analysisand/or boundary conditions may be adjusted based on the comparison.

D. Another Embodiment of a System and Method for Providing CoronaryBlood Flow Information

Another embodiment of a method 600 for providing various informationrelating to coronary blood flow in a specific patient is shown in FIG.24. The method 600 may be implemented in the computer system describedabove, e.g., the computer system used to implement one or more of thesteps described above and shown in FIG. 3. The method 600 may beperformed using one or more inputs 610, and may include generating oneor more models 620 based on the inputs 610, assigning one or moreconditions 630 based on the inputs 610 and/or the models 620, andderiving one or more solutions 640 based on the models 620 and theconditions 630.

The inputs 610 may include medical imaging data 611 of the patient'saorta, coronary arteries (and the branches that extend therefrom), andheart, such as CCTA data (e.g., obtained in step 100 of FIG. 2). Theinputs 610 may also include a measurement 612 of the patient's brachialblood pressure and/or other measurements (e.g., obtained in step 100 ofFIG. 2). The measurements 612 may be obtained noninvasively. The inputs610 may be used to generate the model(s) 620 and/or determine thecondition(s) 630 described below.

As noted above, one or more models 620 may be generated based on theinputs 610. For example, the method 600 may include generating one ormore patient-specific three-dimensional geometric models of thepatient's anatomy (e.g., the aorta, coronary arteries, and branches thatextend therefrom) based on the imaging data 611 (step 621). For example,the geometric model may be the solid model 320 of FIG. 8 generated instep 306 of FIG. 3, and/or the mesh 380 of FIGS. 17-19 generated in step312 of FIG. 3.

Referring back to FIG. 24, the method 600 may also include generatingone or more physics-based blood flow models (step 622). The blood flowmodels may include a model that relates to blood flow through thepatient-specific geometric model generated in step 621, heart and aorticcirculation, distal coronary circulation, etc. The blood flow models mayrelate to at least one blood flow characteristic associated with thepatient's modeled anatomy, e.g., blood flow velocity, pressure, flowrate, FFR, etc. The blood flow models may be assigned as boundaryconditions at the inflow and outflow boundaries 322, 324 of thethree-dimensional geometric model. The blood flow model may include thereduced order models or other boundary conditions described above inconnection with step 310 of FIG. 3, e.g., the lumped parameter heartmodel 340, the lumped parameter coronary model 350, the Windkessel model360, etc.

As noted above, one or more conditions 630 may be determined based onthe inputs 610 and/or the models 620. The conditions 630 include theparameters calculated for the boundary conditions determined in step 622(and step 310 of FIG. 3). For example, the method 600 may includedetermining a condition by calculating a patient-specific ventricular ormyocardial mass based on the imaging data 611 (e.g., as determined instep 240 of FIG. 3) (step 631).

The method 600 may include determining a condition by calculating, usingthe ventricular or myocardial mass calculated in step 631, a restingcoronary flow based on the relationship Q=Q_(o)M^(α), where α is apreset scaling exponent, M is the ventricular or myocardial mass, andQ_(o) is a preset constant (e.g., as described above in connection withdetermining the lumped parameter model in step 310 of FIG. 3) (step632). Alternatively, the relationship may have the form Q∝Q_(o)M^(α), asdescribed above in connection with determining the lumped parametermodel in step 310 of FIG. 3.

The method 600 may also include determining a condition by calculating,using the resulting coronary flow calculated in step 632 and thepatient's measured blood pressure 612, a total resting coronaryresistance (e.g., as described above in connection with determining thelumped parameter model in step 310 of FIG. 3) (step 633).

The method 600 may also include determining a condition by calculating,using the total resting coronary resistance calculated in step 633 andthe models 620, individual resistances for the individual coronaryarteries (and the branches that extend therefrom) (step 634). Forexample, as described above in connection with step 310 of FIG. 3, thetotal resting coronary resistance calculated in step 633 may bedistributed to the individual coronary arteries and branches based onthe sizes (e.g., determined from the geometric model generated in step621) of the distal ends of the individual coronary arteries andbranches, and based on the relationship R=R_(o)d^(β), where R is theresistance to flow at a particular distal end, and R_(o) is a presetconstant, d is the size (e.g., diameter of that distal end), and β is apreset power law exponent, as described above in connection withdetermining the lumped parameter model in step 310 of FIG. 3.

Referring back to FIG. 24, the method 600 may include adjusting theboundary conditions based on one or more physical conditions of thepatient (step 635). For example, the parameters determined in steps631-634 may be modified based on whether the solution 640 is intended tosimulate rest, varying levels of hyperemia, varying levels of exerciseor exertion, different medications, etc. Based on the inputs 610, themodels 620, and the conditions 630, a computational analysis may beperformed, e.g., as described above in connection with step 402 of FIG.3, to determine the solution 640 that includes information about thepatient's coronary blood flow under the physical conditions selected instep 635 (step 641). Examples of information that may be provided fromthe solution 640 will now be described.

The combined patient-specific anatomic (geometric) and physiologic(physics-based) model may be used to determine the effect of differentmedications or lifestyle changes (e.g., cessation of smoking, changes indiet, or increased physical activity) that alters heart rate, strokevolume, blood pressure, or coronary microcirculatory function oncoronary artery blood flow. Such information may be used to optimizemedical therapy or avert potentially dangerous consequences ofmedications. The combined model may also be used to determine the effecton coronary artery blood flow of alternate forms and/or varying levelsof physical activity or risk of exposure to potential extrinsic force,e.g., when playing football, during space flight, when scuba diving,during airplane flights, etc. Such information may be used to identifythe types and level of physical activity that may be safe andefficacious for a specific patient. The combined model may also be usedto predict a potential benefit of percutaneous coronary interventions oncoronary artery blood flow in order to select the optimal interventionalstrategy, and/or to predict a potential benefit of coronary arterybypass grafting on coronary artery blood flow in order to select theoptimal surgical strategy.

The combined model may also be used to illustrate potential deleteriouseffects of an increase in the burden of arterial disease on coronaryartery blood flow and to predict, using mechanistic or phenomenologicaldisease progression models or empirical data, when advancing disease mayresult in a compromise of blood flow to the heart muscle. Suchinformation may enable the determination of a “warranty period” in whicha patient observed to be initially free from hemodynamically significantdisease using noninvasive imaging may not be expected to requiremedical, interventional, or surgical therapy, or alternatively, the rateat which progression might occur if adverse factors are continued.

The combined model may also be used to illustrate potential beneficialeffects on coronary artery blood flow resulting from a decrease in theburden of coronary artery disease and to predict, using mechanistic orphenomenological disease progression models or empirical data, whenregression of disease may result in increased blood flow through thecoronary arteries to the heart muscle. Such information may be used toguide medical management programs including, but not limited to, changesin diet, increased physical activity, prescription of statins or othermedications, etc.

VI. Providing Patient-Specific Treatment Planning

As described above in connection with step 500 shown in FIG. 2, theexemplary method may include providing patient-specific treatmentplanning. In an exemplary embodiment, step 500 may include the followingsteps. Although FIG. 3 does not show the following steps, it isunderstood that these steps may be performed in conjunction with thesteps shown in FIG. 3, e.g., after steps 406 or 408.

As described above, the cFFR model 54 shown in FIGS. 1 and 23 indicatesthe cFFR values throughout the patient's anatomy represented by the mesh380 of FIGS. 17-19 in an untreated state and under simulated hyperemiaconditions. Using this information, the physician may prescribetreatments to the patient, such as an increase in exercise, a change indiet, a prescription of medication, surgery on any portion of themodeled anatomy or other portions of the heart (e.g., coronary arterybypass grafting, insertion of one or more coronary stents, etc.), etc.

To determine which treatment(s) to prescribe, the computer system may beused to predict how the information determined from the computationalanalysis would change based on such treatment(s). For example, certaintreatments, such as insertion of stent(s) or other surgeries, may resultin a change in geometry of the modeled anatomy. Accordingly, in anexemplary embodiment, the solid model 320 generated in step 306 may berevised to indicate a widening of one or more lumens where a stent isinserted.

For example, the cFFR model 54 shown in FIGS. 1 and 23 indicates thatthe lowest cFFR value in the LAD artery is 0.66, the lowest cFFR valuein the LCX artery is 0.72, the lowest cFFR value in the RCA artery is0.80. Treatment may be proposed if a cFFR value is, for example, lessthan 0.75. Accordingly, the computer system may propose to the userrevising the solid model 320 to indicate a widening of the LAD arteryand the LCX artery to simulate inserting stents in these coronaryarteries. The user may be prompted to choose the location and amount ofwidening (e.g., the length and diameter) corresponding to the locationand size of the simulated stent. Alternatively, the location and amountof widening may be determined automatically by the computer system basedon various factors, such as the location of the node(s) with cFFR valuesthat are less than 0.75, a location of a significant narrowing of thevessels, sizes of conventional stents, etc.

FIG. 25 shows an example of a modified cFFR model 510 determined basedon a solid model created by widening a portion of the LAD artery atlocation 512 and a portion of the LCX artery at location 514. In anexemplary embodiment, any of the steps described above, e.g., steps310-314 and 402-408, may be repeated using the modified solid model. Instep 406, the finalized report may include the information relating tothe untreated patient (e.g., without the stents), such as theinformation shown in FIG. 23, and information relating to the simulatedtreatment for the patient, such as the information shown in FIGS. 25 and26.

FIG. 25 includes the modified cFFR model 510 and also includes summaryinformation, such as the lowest cFFR values in the main coronaryarteries and the branches that extend therefrom for the modified solidmodel associated with the proposed treatment. For example, FIG. 25indicates that the lowest cFFR value in the LAD artery (and itsdownstream branches) is 0.78, the lowest cFFR value in the LCX artery(and its downstream branches) is 0.78, the lowest cFFR value in the RCAartery (and its downstream branches) is 0.79. Accordingly, a comparisonof the cFFR model 54 of the untreated patient (without stents) and thecFFR model 510 for the proposed treatment (with stents inserted)indicates that the proposed treatment may increase the minimum cFFR inthe LAD artery from 0.66 to 0.78 and would increase the minimum cFFR inthe LCX artery from 0.72 to 0.76, while there would be a minimaldecrease in the minimum cFFR in the RCA artery from 0.80 to 0.79.

FIG. 26 shows an example of a modified simulated blood flow model 520determined after widening portions of the LAD artery at location 512 andof the LCX artery at location 514 as described above. FIG. 26 alsoincludes summary information, such as the blood flow values at variouslocations in the main coronary arteries and the branches that extendtherefrom for the modified solid model associated with the proposedtreatment. For example, FIG. 26 indicates blood flow values for fourlocations LAD1, LAD2, LAD3, and LAD4 in the LAD artery and for twolocations LCX1 and LCX2 in the LCX artery for the untreated patient(without stents) and for the treated patient (with stents inserted).FIG. 26 also indicates a percentage change in blood flow values betweenthe untreated and treated states. Accordingly, a comparison of thesimulated blood flow model 52 of the untreated patient and the simulatedblood flow model 520 for the proposed treatment indicates that theproposed treatment may increase the flow through the LAD artery and LCXartery at all of the locations LAD1-LAD4, LCX1, and LCX2 by 9% to 19%,depending on the location.

Other information may also be compared between the untreated and treatedstates, such as coronary artery blood pressure. Based on thisinformation, the physician may discuss with the patient whether toproceed with the proposed treatment option.

Other treatment options may also involve modifying the solid model 320in different ways. For example, coronary artery bypass grafting mayinvolve creating new lumens or passageways in the solid model 320 andremoving a lesion may also involve widening a lumen or passage. Othertreatment options may not involve modifying the solid model 320. Forexample, an increase in exercise or exertion, a change in diet or otherlifestyle change, a prescription of medication, etc., may involvechanging the boundary conditions determined in step 310, e.g., due tovasoconstriction, dilation, decreased heart rate, etc. For example, thepatient's heart rate, cardiac output, stroke volume, blood pressure,coronary microcirculation function, the configurations of the lumpedparameter models, etc., may depend on the medication prescribed, thetype and frequency of exercise adopted (or other exertion), the type oflifestyle change adopted (e.g., cessation of smoking, changes in diet,etc.), thereby affecting the boundary conditions determined in step 310in different ways.

In an exemplary embodiment, modified boundary conditions may bedetermined experimentally using data from many patients, and similartreatment options may require modifying the boundary conditions insimilar ways. Empirical models may be developed from a large populationof patient-specific data, creating a library of boundary conditions orfunctions for calculating boundary conditions, corresponding to specifictreatment options that may be applied to similar patients in futureanalyses.

After modifying the boundary conditions, the steps described above,e.g., steps 312, 314, and 402-408, may be repeated using the modifiedboundary conditions, and in step 406, the finalized report may includethe information relating to the untreated patient, such as theinformation shown in FIG. 23, and information relating to the simulatedtreatment for the patient, such as the information shown in FIGS. 25 and26.

Alternatively, the physician, the patient, or other user may be providedwith a user interface that allows interaction with a three-dimensionalmodel (e.g., the solid model 320 of FIG. 8). The model 320 may bedivided into user-selectable segments that may be edited by the user toreflect one or more treatment options. For example, the user may selecta segment with a stenosis (or occlusion, e.g., an acute occlusion) andadjust the segment to remove the stenosis, the user may add a segment tothe model 320 to serve as a bypass, etc. The user may also be promptedto specify other treatment options and/or physiologic parameters thatmay alter the boundary conditions determined above, e.g., a change in acardiac output, a heart rate, a stroke volume, a blood pressure, anexercise or exertion level, a hyperemia level, medications, etc. In analternate embodiment, the computer system may determine or suggest atreatment option.

The user interface may allow interaction with the three-dimensionalmodel 320 to allow the user to simulate a stenosis (or occlusion, e.g.,an acute occlusion). For example, the user may select a segment forincluding the stenosis, and the computer system may be used to predicthow the information determined from the computational analysis wouldchange based on the addition of the stenosis. Thus, the methodsdescribed herein may be used to predict the effect of occluding anartery.

The user interface may also allow interaction with the three-dimensionalmodel 320 to simulate a damaged artery or removal of an artery, whichmay occur, for example, in certain surgical procedures, such as whenremoving cancerous tumors. The model may also be modified to simulatethe effect of preventing blood flow through certain arteries in order topredict the potential for collateral pathways for supplying adequateblood flow for the patient.

A. Using Reduced Order Models to Compare Different Treatment Options

In an exemplary embodiment, the computer system may allow the user tosimulate various treatment options more quickly by replacing thethree-dimensional solid model 320 or mesh 380 with a reduced ordermodel. FIG. 27 shows a schematic diagram relating to a method 700 forsimulating various treatment options using a reduced order model,according to an exemplary embodiment. The method 700 may be implementedin the computer system described above.

One or more patient-specific simulated blood flow models representingblood flow or other parameters may be output from the computationalanalysis described above (step 701). For example, the simulated bloodflow models may include the simulated blood pressure model 50 of FIG. 1,the simulated blood flow model 52 of FIG. 1, the cFFR model 54 of FIG.1, etc., provided using the methods described above and shown in FIGS. 2and 3. As described above, the simulated blood flow model may include athree-dimensional geometrical model of the patient's anatomy.

Functional information may be extracted from the simulated blood flowmodels in order to specify conditions for a reduced order model (step702). For example, the functional information may include the bloodpressure, flow, or velocity information determined using thecomputational analysis described above.

A reduced order (e.g., zero-dimensional or one-dimensional) model may beprovided to replace the three-dimensional solid model 320 used togenerate the patient specific simulated blood flow models generated instep 701, and the reduced order model may be used to determineinformation about the coronary blood flow in the patient (step 703). Forexample, the reduced order model may be a lumped parameter modelgenerated as described above in connection with step 310 of FIG. 3.Thus, the lumped parameter model is a simplified model of the patient'sanatomy that may be used to determine information about the coronaryblood flow in the patient without having to solve the more complexsystem of equations associated with the mesh 380 of FIGS. 17-19.

Information determined from solving the reduced order model in step 703may then be mapped or extrapolated to a three-dimensional solid model(e.g., the solid model 320) of the patient's anatomy (step 704), and theuser may make changes to the reduced order model as desired to simulatevarious treatment options and/or changes to the physiologic parametersfor the patient, which may be selected by the user (step 705). Theselectable physiologic parameters may include cardiac output, exerciseor exertion level, level of hyperemia, types of medications, etc. Theselectable treatment options may include removing a stenosis, adding abypass, etc.

Then, the reduced order model may be modified based on the treatmentoptions and/or physiologic parameters selected by the user, and themodified reduced order model may be used to determine information aboutthe coronary blood flow in the patient associated with the selectedtreatment option and/or physiologic parameter (step 703). Informationdetermined from solving the reduced order model in step 703 may then bemapped or extrapolated to the three-dimensional solid model 320 of thepatient's anatomy to predict the effects of the selected treatmentoption and/or physiologic parameter on the coronary blood flow in thepatient's anatomy (step 704).

Steps 703-705 may be repeated for various different treatment optionsand/or physiologic parameters to compare the predicted effects ofvarious treatment options to each other and to the information about thecoronary blood flow in the untreated patient. As a result, predictedresults for various treatment options and/or physiologic parameters maybe evaluated against each other and against information about theuntreated patient without having to rerun the more complex analysisusing the three-dimensional mesh 380. Instead, a reduced order model maybe used, which may allow the user to analyze and compare differenttreatment options and/or physiologic parameters more easily and quickly.

FIG. 28 shows further aspects of the exemplary method for simulatingvarious treatment options using a reduced order model, according to anexemplary embodiment. The method 700 may be implemented in the computersystem described above.

As described above in connection with step 306 of FIG. 3, apatient-specific geometric model may be generated based on imaging datafor the patient (step 711). For example, the imaging data may includethe CCTA data obtained in step 100 of FIG. 2, and the geometric modelmay be the solid model 320 of FIG. 8 generated in step 306 of FIG. 3,and/or the mesh 380 of FIGS. 17-19 generated in step 312 of FIG. 3.

Using the patient-specific three-dimensional geometric model, thecomputational analysis may be performed, e.g., as described above inconnection with step 402 of FIG. 3, to determine information about thepatient's coronary blood flow (step 712). The computational analysis mayoutput one or more three-dimensional patient-specific simulated bloodflow models representing blood flow or other parameters, e.g., thesimulated blood pressure model 50 of FIG. 1, the simulated blood flowmodel 52 of FIG. 1, the cFFR model 54 of FIG. 1, etc.

The simulated blood flow model may be segmented (e.g., as describedabove in connection with FIG. 14) based on the anatomical features ofthe model (step 713). For example, branches extending from the maincoronary arteries may be provided in separate segments (step 714),portions with stenosis or diseased areas may be provided in separatesegments (step 716), and portions between the branches and the portionswith stenosis or diseased areas may be provided in separate segments(step 715). Varying degrees of resolution may be provided in segmentingthe simulated blood flow model such that each vessel may include aplurality of short, discrete segments or longer segments, e.g.,including the entire vessel. Also, various techniques may be providedfor segmenting the simulated blood flow model, including generatingcenterlines and sectioning based on the generated centerlines, ordetecting branch points and sectioning based on the detected branchpoints. The diseased portions and stenoses may be identified, e.g., bymeasuring the cross-sectional area along the length of the centerlineand calculating locally minimum cross-sectional areas. Steps 711-716 maybe considered as substeps of step 701 of FIG. 27.

The segments may be replaced by components of a lumped parameter model,such as resistors, capacitors, inductors, etc., as described above inconnection with FIG. 15. The individual values for the resistance,capacitance, inductance, and other variables associated with otherelectrical components used in the lumped parameter model may be derivedfrom the simulated blood flow models provided in step 712. For example,for branches and portions between the branches and the portions withstenosis or diseased areas, information derived from the simulated bloodflow model may be used to assign linear resistances to the correspondingsegments (step 717). For portions with complex geometry, such as astenosis or diseased area, resistance may vary with flow rate. Thus,multiple computational analyses may be used to obtain simulated bloodflow models for various flow and pressure conditions to derivepatient-specific, vessel-specific, and lesion-specific resistancefunctions for these complex geometries, as described above in connectionwith FIG. 15. Accordingly, for portions with stenosis or diseased areas,information derived from these multiple computational analyses or modelsderived from previous data may be used to assign non-linear,flow-dependent resistances to corresponding segments (step 718). Steps717 and 718 may be considered as substeps of step 702 of FIG. 27.

Using the resistances determined in steps 717 and 718, a reduced order(e.g., zero-dimensional or one-dimensional) model may be generated (step719). For example, the reduced order model may be a lumped parametermodel generated as described above in connection with step 310 of FIG.3. Thus, the lumped parameter model is a simplified model of thepatient's anatomy that may be used to determine information about thecoronary blood flow in the patient without having to solve the morecomplex system of equations associated with the mesh 380 of FIGS. 17-19.

A user interface may be provided that allows the user to interact withthe reduced order model created in step 719 (step 720). For example, theuser may select and edit different segments of the reduced order modelto simulate different treatment options and/or may edit variousphysiologic parameters. For example, intervention, such as insertion ofa stent to repair of a diseased region, may be modeled by decreasing theresistance of the segment where the stent is to be inserted. Forming abypass may be modeled by adding a segment having a low resistanceparallel to a diseased segment.

The modified reduced order model may be solved to determine informationabout the coronary blood flow in the patient under the treatment and/orchange in physiologic parameters selected in step 720 (step 721). Thesolution values for flow and pressure in each segment determined in step721 may then be compared to the three-dimensional solution determined instep 712, and any difference may be minimized by adjusting theresistance functions of the segments (e.g., as determined in steps 717and 718) and resolving the reduced order model (e.g., step 721) untilthe solutions match. As a result, the reduced order model may be createdand then solved with a simplified set of equations that allows forrelatively rapid computation (e.g., compared to a full three-dimensionalmodel) and may be used to solve for flow rate and pressure that mayclosely approximate the results of a full three-dimensionalcomputational solution. The reduced order model allows for relativelyrapid iterations to model various different treatment options.

Information determined from solving the reduced order model in step 721may then be mapped or extrapolated to a three-dimensional solid model ofthe patient's anatomy (e.g., the solid model 320) (step 722). Steps719-722 may be similar to steps 703-705 of FIG. 27 and may be repeatedas desired by the user to simulate different combinations of treatmentoptions and/or physiologic parameters.

Alternatively, rather than calculating the resistance along segmentsfrom the three-dimensional model (e.g., as described above for steps 717and 718), flow and pressure at intervals along the centerline may beprescribed into a lumped parameter or one-dimensional model. Theeffective resistances or loss coefficients may be solved for under theconstraints of the boundary conditions and prescribed flow and pressure.

Also, the flow rates and pressure gradients across individual segmentsmay be used to compute an epicardial coronary resistance using thesolution derived from the reduced-order model (e.g., as described abovefor step 721). The epicardial coronary resistance may be calculated asan equivalent resistance of the epicardial coronary arteries (theportions of the coronary arteries and the branches that extend therefromincluded in the patient-specific model reconstructed from medicalimaging data). This may have clinical significance in explaining whypatients with diffuse atherosclerosis in the coronary arteries mayexhibit symptoms of ischemia (restriction in blood supply). Also, theflow per unit of myocardial tissue volume (or mass) and/or the flow perunit of cardiac work under conditions of simulatedpharmacologically-induced hyperemia or varying exercise intensity may becalculated using data from the reduced-order models.

As a result, the accuracy of three-dimensional blood flow modeling maybe combined with the computational simplicity and relative speedinherent in one-dimensional and lumped parameter modeling technologies.Three-dimensional computational methods may be used to numericallyderive patient-specific one-dimensional or lumped parameter models thatembed numerically-derived empirical models for pressure losses overnormal segments, stenoses, junctions, and other anatomical features.Improved diagnosis for patients with cardiovascular disease may beprovided, and planning of medical, interventional, and surgicaltreatments may be performed faster.

Also, the accuracy of three-dimensional computational fluid dynamicstechnologies may be combined with the computational simplicity andperformance capabilities of lumped parameter and one-dimensional modelsof blood flow. A three-dimensional geometric and physiologic model maybe decomposed automatically into a reduced-order one-dimensional orlumped parameter model. The three-dimensional model may be used tocompute the linear or nonlinear hemodynamic effects of blood flowthrough normal segments, stenoses, and/or branches, and to set theparameters of empirical models. The one-dimensional or lumped parametermodels may more efficiently and rapidly solve for blood flow andpressure in a patient-specific model, and display the results of thelumped parameter or one-dimensional solutions.

The reduced order patient-specific anatomic and physiologic model may beused to determine the effect of different medications or lifestylechanges (e.g., cessation of smoking, changes in diet, or increasedphysical activity) that alters heart rate, stroke volume, bloodpressure, or coronary microcirculatory function on coronary artery bloodflow. Such information may be used to optimize medical therapy or avertpotentially dangerous consequences of medications. The reduced ordermodel may also be used to determine the effect on coronary artery bloodflow of alternate forms and/or varying levels of physical activity orrisk of exposure to potential extrinsic force, e.g., when playingfootball, during space flight, when scuba diving, during airplaneflights, etc. Such information may be used to identify the types andlevel of physical activity that may be safe and efficacious for aspecific patient. The reduced order model may also be used to predict apotential benefit of percutaneous coronary interventions on coronaryartery blood flow in order to select the optimal interventionalstrategy, and/or to predict a potential benefit of coronary arterybypass grafting on coronary artery blood flow in order to select theoptimal surgical strategy.

The reduced order model may also be used to illustrate potentialdeleterious effects of an increase in the burden of arterial disease oncoronary artery blood flow and to predict, using mechanistic orphenomenological disease progression models or empirical data, whenadvancing disease may result in a compromise of blood flow to the heartmuscle. Such information may enable the determination of a “warrantyperiod” in which a patient observed to be initially free fromhemodynamically significant disease using noninvasive imaging may not beexpected to require medical, interventional, or surgical therapy, oralternatively, the rate at which progression might occur if adversefactors are continued.

The reduced order model may also be used to illustrate potentialbeneficial effects on coronary artery blood flow resulting from adecrease in the burden of coronary artery disease and to predict, usingmechanistic or phenomenological disease progression models or empiricaldata, when regression of disease may result in increased blood flowthrough the coronary arteries to the heart muscle. Such information maybe used to guide medical management programs including, but not limitedto, changes in diet, increased physical activity, prescription ofstatins or other medications, etc.

The reduced order model may also be incorporated into an angiographysystem to allow for live computation of treatment options while aphysician examines a patient in a cardiac catheterization lab. The modelmay be registered to the same orientation as the angiography display,allowing side-by-side or overlapping results of a live angiographic viewof the coronary arteries with simulated blood flow solutions. Thephysician may plan and alter treatment plans as observations are madeduring procedures, allowing for relatively rapid feedback before medicaldecisions are made. The physician may take pressure, FFR, or blood flowmeasurements invasively, and the measurements may be utilized to furtherrefine the model before predictive simulations are performed.

The reduced order model may also be incorporated into a medical imagingsystem or workstation. If derived from a library of previouspatient-specific simulation results, then the reduced order models maybe used in conjunction with geometric segmentation algorithms torelatively rapidly solve for blood flow information after completing animaging scan.

The reduced order model may also be used to model the effectiveness ofnew medical therapies or the cost/benefit of treatment options on largepopulations of patients. A database of multiple patient-specific lumpedparameter models (e.g., hundreds, thousands, or more) may provide modelsto solve in relatively short amounts of time. Relatively quick iterationand optimization may be provided for drug, therapy, or clinical trialsimulation or design. Adapting the models to represent treatments,patient responses to drugs, or surgical interventions may allowestimates of effectiveness to be obtained without the need to performpossibly costly and potentially risky large-scale clinical trials.

VII. Other Results

A. Assessing Myocardial Perfusion

Other results may be calculated. For example, the computational analysismay provide results that quantify myocardial perfusion (blood flowthrough the myocardium). Quantifying myocardial perfusion may assist inidentifying areas of reduced myocardial blood flow, such as due toischemia (a restriction in a blood supply), scarring, or other heartproblems.

FIG. 29 shows a schematic diagram relating to a method 800 for providingvarious information relating to myocardial perfusion in a specificpatient, according to an exemplary embodiment. The method 800 may beimplemented in the computer system described above, e.g., the computersystem used to implement one or more of the steps described above andshown in FIG. 3.

The method 800 may be performed using one or more inputs 802. The inputs802 may include medical imaging data 803 of the patient's aorta,coronary arteries (and the branches that extend therefrom), and heart,such as CCTA data (e.g., obtained in step 100 of FIG. 2). The inputs 802may also include additional physiological data 804 measured from thepatient, such as the patient's brachial blood pressure, heart rate,and/or other measurements (e.g., obtained in step 100 of FIG. 2). Theadditional physiological data 804 may be obtained noninvasively. Theinputs 802 may be used to perform the steps described below.

A three-dimensional geometric model of the patient's myocardial tissuemay be created based on the imaging data 803 (step 810) and thegeometric model may be divided into segments or volumes (step 812). Forexample, FIG. 31 shows a three-dimensional geometric model 846 includinga three-dimensional geometric model 838 of the patient's myocardialtissue divided into segments 842. The sizes and locations of theindividual segments 842 may be determined based on the locations of theoutflow boundaries 324 (FIG. 8) of the coronary arteries (and thebranches extending therefrom), the sizes of the blood vessels in orconnected to the respective segment 842 (e.g., the neighboring bloodvessels), etc. The division of the geometric myocardial model 838 intosegments 842 may be performed using various known methods, such as afast marching method, a generalized fast marching method, a level setmethod, a diffusion equation, equations governing flow through a porousmedia, etc.

The three-dimensional geometric model may also include a portion of thepatient's aorta and coronary arteries (and the branches that extendtherefrom), which may be modeled based on the imaging data 803 (step814). For example, the three-dimensional geometric model 846 of FIG. 31includes a three-dimensional geometric model 837 of the patient's aortaand coronary arteries (and the branches that extend therefrom) and thethree-dimensional geometric model 838 of the patient's myocardial tissuecreated in step 810.

Referring back to FIG. 29, a computational analysis may be performed,e.g., as described above in connection with step 402 of FIG. 3, todetermine a solution that includes information about the patient'scoronary blood flow under a physical condition determined by the user(step 816). For example, the physical condition may include rest, aselected level of hyperemia, a selected level of exercise or exertion,or other conditions. The solution may provide information, such as bloodflow and pressure, at various locations in the anatomy of the patientmodeled in step 814 and under the specified physical condition. Thecomputational analysis may be performed using boundary conditions at theoutflow boundaries 324 (FIG. 8) derived from lumped parameter orone-dimensional models. The one-dimensional models may be generated tofill the segments 842 as described below in connection with FIG. 30.

Based on the blood flow information determined in step 816, theperfusion of blood flow into the respective segments 842 of themyocardium created in step 812 may be calculated (step 818). Forexample, the perfusion may be calculated by dividing the flow from eachoutlet of the outflow boundaries 324 (FIG. 8) by the volume of thesegmented myocardium to which the outlet perfuses.

The perfusion for the respective segments of the myocardium determinedin step 818 may be displayed on the geometric model of the myocardiumgenerated in step 810 or 812 (e.g., the three-dimensional geometricmodel 838 of the patient's myocardial tissue shown in FIG. 31) (step820). For example, FIG. 31 shows that the segments 842 of the myocardiumof the geometric model 838 may be illustrated with a different shade orcolor to indicate the perfusion of blood flow into the respectivesegments 842.

FIG. 30 shows another schematic diagram relating to a method 820 forproviding various information relating to myocardial perfusion in aspecific patient, according to an exemplary embodiment. The method 820may be implemented in the computer system described above, e.g., thecomputer system used to implement one or more of the steps describedabove and shown in FIG. 3.

The method 820 may be performed using one or more inputs 832, which mayinclude medical imaging data 833 of the patient's aorta, coronaryarteries (and the branches that extend therefrom), and heart, such asCCTA data (e.g., obtained in step 100 of FIG. 2). The inputs 832 may beused to perform the steps described below.

A three-dimensional geometric model of the patient's myocardial tissuemay be created based on the imaging data 833 (step 835). The model mayalso include a portion of the patient's aorta and coronary arteries (andthe branches that extend therefrom), which may also be created based onthe imaging data 803. For example, as described above, FIG. 31 shows athree-dimensional geometric model 836 including the geometric model 837of the patient's aorta and coronary arteries (and the branches thatextend therefrom) and the geometric model 838 of the patient'smyocardial tissue. Step 835 may include steps 810 and 814 of FIG. 29described above.

Referring back to FIG. 30, the geometric myocardial model 838 may bedivided into volumes or segments 842 (step 840). Step 840 may includestep 812 of FIG. 29 described above. As described above, FIG. 31 showsthe three-dimensional geometric model 846 including the geometric model838 of the patient's myocardial tissue divided into the segments 842.

Referring back to FIG. 30, the geometric model 846 may be modified toinclude a next generation of branches 857 in the coronary tree (step855). The location and size of the branches 857 (shown in dashed linesin FIG. 31) may be determined based on centerlines for the coronaryarteries (and the branches that extend therefrom). The centerlines maybe determined, e.g., based on the imaging data 833 (step 845). Analgorithm may also be used to determine the location and size of thebranches 857 based on morphometric models (models used to predict vessellocation and size downstream of the known outlets at the outflowboundaries 324 (FIG. 8)) and/or physiologic branching laws related tovessel size (step 850). The morphometric model may be augmented to thedownstream ends of the coronary arteries (and the branches that extendtherefrom) included in the geometric model 837, and provided on theepicardial surface (the outer layer of heart tissue) or contained withinthe geometric model 838 of the myocardial wall.

The myocardium may be further segmented based on the branches 857created in step 855 (step 860). For example, FIG. 31 shows that segments842 may be divided into subvolumes or subsegments 862.

Additional branches 857 may be created in the subsegments 862, and thesubsegments 862 may be further segmented into smaller segments 867 (step865). The steps of creating branches and sub-segmenting the volumes maybe repeated until a desired resolution of volume size and/or branch sizeis obtained. The model 846, which has been augmented to include newbranches 857 in steps 855 and 865, may then be used to compute coronaryblood flow and myocardial perfusion into the subsegments, such as thesubsegments 867 generated in step 865.

Accordingly, the augmented model may be used to perform thecomputational analysis described above. The results of the computationalanalysis may provide information relating to the blood flow from thepatient-specific coronary artery model, e.g., the model 837 of FIG. 31,into the generated morphometric model (including the branches 857generated in steps 855 and 865), which may extend into each of theperfusion subsegments 867 generated in step 865. The computationalanalysis may be performed using a static myocardial perfusion volume ora dynamic model incorporating data from coupled cardiac mechanicsmodels.

FIG. 32 shows another schematic diagram relating to a method 870 forproviding various information relating to myocardial perfusion in aspecific patient, according to an exemplary embodiment. The method 870may be implemented in the computer system described above, e.g., thecomputer system used to implement one or more of the steps describedabove and shown in FIG. 3.

The method 870 may be performed using one or more inputs 872. The inputs872 may include medical imaging data 873 of the patient's aorta,coronary arteries (and the branches that extend therefrom), and heart,such as CCTA data (e.g., obtained in step 100 of FIG. 2). The inputs 872may also include additional physiological data 874 measured from thepatient, such as the patient's brachial blood pressure, heart rate,and/or other measurements (e.g., obtained in step 100 of FIG. 2). Theadditional physiological data 874 may be obtained noninvasively. Theinputs 872 may further include cardiac perfusion data 875 measured fromthe patient (e.g., using CT, PET, SPECT, etc.). The inputs 872 may beused to perform the steps described below.

A three-dimensional geometric model of the patient's aorta and coronaryarteries (and the branches that extend therefrom) may be created basedon the imaging data 873 (step 880). For example, FIG. 31 shows thethree-dimensional geometric model 837 of the patient's aorta andcoronary arteries (and the branches that extend therefrom). Step 880 maybe similar to step 814 of FIG. 29 described above.

A computational analysis may be performed, e.g., as described above inconnection with step 402 of FIG. 3, to determine a solution thatincludes information about the patient's coronary blood flow under aphysical condition determined by the user (step 882). For example, thephysical condition may include rest, a selected level of hyperemia, aselected level of exercise or exertion, or other conditions. Thesolution may provide information, such as blood flow and pressure, atvarious locations in the anatomy of the patient modeled in step 880 andunder the specified physical condition. Step 882 may be similar to step816 of FIG. 29 described above.

Also, a three-dimensional geometric model of the patient's myocardialtissue may be created based on the imaging data 873 (step 884). Forexample, as described above, FIG. 31 shows the three-dimensionalgeometric model 836 including the three-dimensional geometric model 838of the patient's myocardial tissue (e.g., as created in step 884) andthe three-dimensional geometric model 837 of the patient's aorta andcoronary arteries (and the branches that extend therefrom) (e.g., ascreated in step 880). Step 884 may be similar to step 810 of FIG. 29described above.

The geometric model may be divided into segments or subvolumes (step886). For example, FIG. 31 shows the geometric model 846 including themodel 838 of the patient's myocardial tissue divided into segments 842.Step 886 may be similar to step 812 of FIG. 29 described above.

Based on the blood flow information determined in step 882, theperfusion of blood flow into the respective segments 842 of themyocardium created in step 886 may be calculated (step 888). Step 888may be similar to step 818 of FIG. 29 described above.

The calculated perfusion for the respective segments of the myocardiummay be displayed on the geometric model of the myocardium generated instep 884 or 886 (e.g., the three-dimensional geometric model 838 of thepatient's myocardial tissue shown in FIG. 31) (step 890). For example,FIG. 31 shows that the segments 842 of the myocardium of the geometricmodel 838 may be illustrated with a different shade or color to indicatethe perfusion of blood flow into the respective segments 842. Step 890may be similar to step 820 of FIG. 29 described above.

The simulated perfusion data mapped onto the three-dimensional geometricmodel of the myocardium in step 890 may be compared with the measuredcardiac perfusion data 875 (step 892). The comparison may be performed,e.g., on a voxel-based representation of the myocardium or a differentdiscrete representation of the myocardium, e.g. a finite element mesh.The comparison may indicate the differences in the simulated andmeasured perfusion data using various colors and/or shades on thethree-dimensional representation of the myocardium.

The boundary conditions at the outlets of the three-dimensionalgeometric model created in step 880 may be adjusted to decrease theerror between the simulated and measured perfusion data (step 894). Forexample, in order to reduce the error, the boundary conditions may beadjusted so that the prescribed resistance to flow of the vesselsfeeding a region (e.g., the segment 842, 862, or 867) where thesimulated perfusion is lower than the measured perfusion may be reduced.Other parameters of the boundary conditions may be adjusted.Alternatively, the branching structure of the model may be modified. Forexample, the geometric model created in step 880 may be augmented asdescribed above in connection with FIGS. 30 and 31 to create themorphometric model. The parameters of the boundary conditions and/ormorphometric models may be adjusted empirically or systematically usinga parameter estimation or data assimilation method, such as the methoddescribed in U.S. Patent Application Publication No. 2010/0017171, whichis entitled “Method for Tuning Patient-Specific CardiovascularSimulations,” or other methods.

Steps 882, 888, 890, 892, 894, and/or other steps of FIG. 32 may berepeated, e.g., until the error between the simulated and measuredperfusion data is below a predetermined threshold. As a result, thecomputational analysis may be performed using a model that relatesanatomical information, coronary blood flow information, and myocardialperfusion information. Such a model may be useful for diagnosticpurposes and for predicting the benefits of medical, interventional, orsurgical therapies.

As a result, coronary artery blood flow and myocardial perfusion underresting and/or stress conditions may be simulated in a patient-specificgeometric model constructed from three-dimensional medical imaging data.Measured myocardial perfusion data may be used in combination withsimulated myocardial perfusion results to adjust the boundary conditionsuntil the simulated myocardial perfusion results match the measuredmyocardial perfusion data within a given tolerance (e.g., as describedabove in connection with FIG. 32). More accurate patient-specificcoronary artery blood flow computations may be provided, andcardiologists may be enabled to predict coronary artery blood flow andmyocardial perfusion under circumstances where measured data may beunavailable, such as when simulating the patient under maximum exerciseor exertion, simulated treatments, or other conditions.

The patient-specific three-dimensional model of the left and/or rightventricle myocardium may be divided into perfusion segments orsubvolumes. Also, a patient-specific three-dimensional geometric modelof the coronary arteries determined from medical imaging data may becombined with a morphometric model of a portion of the remainingcoronary arterial tree on the epicardial surface or contained in theleft and/or right ventricle myocardial wall represented by the perfusionsubvolumes to form an augmented model. The percentage of the totalmyocardial volume downstream of a given, e.g. diseased, location in theaugmented model may be calculated. The percentage of the totalmyocardial blood flow at a given, e.g., diseased, location in theaugmented model may also be calculated. The augmented model may be usedto compute coronary blood flow and myocardial perfusion. The coronaryblood flow model may also be modified until the simulated perfusionmatches a measured perfusion data within a prescribed tolerance.

B. Assessing Plague Vulnerability

The computational analysis may also provide results that quantifypatient-specific biomechanical forces acting on plaque that may build upin the patient's aorta and coronary arteries (and the branches thatextend therefrom), e.g., coronary atherosclerotic plaque. Thebiomechanical forces may be caused by pulsatile pressure, flow, andheart motion.

FIG. 33 shows an example of plaque 900 built up along a blood vesselwall 902, such as a wall of one of the main coronary arteries or one ofthe branches that extends therefrom. The difference in pressure and/orsurface area between the upstream and downstream ends of the plaque mayproduce a force 904 acting on the plaque 900 at least along thedirection of the blood flow, e.g., caused by the blood flowing throughthe vessel. Another force 906 may act on a surface of the plaque 900 atleast along the direction toward and perpendicular to the vessel wall902. The force 906 may be caused by the blood pressure of the bloodflowing through the vessel. Yet another force 908 may act on the surfaceof the plaque 900 at least along the direction of the blood flow, andmay be due to hemodynamic forces during rest, exercise, etc.

The results may also assess the risk of plaque rupture (e.g., whenplaque accumulated on a vessel wall becomes unstable and breaks off orbreaks open) and the myocardial volume that may be affected by suchrupture. The results may be assessed under various simulatedphysiological conditions, such as resting, exercising, etc. The plaquerupture risk may be defined as a ratio of simulated plaque stress to aplaque strength estimated using material composition data derived fromCCTA or MRI (e.g., determined in step 100 of FIG. 2).

For example, FIG. 34 shows an example of results that the computationalanalysis may output. The results may include the three-dimensionalgeometric model 846 of FIG. 31, which may include the three-dimensionalgeometric model 837 of the patient's aorta and coronary arteries (andthe branches that extend therefrom) and the three-dimensional geometricmodel 838 of the patient's myocardial tissue divided into segments 842.The results may also indicate a location 910 in one of the coronaryarteries (of the branches that extend therefrom) where plaque may bedetermined to be vulnerable, and the location 910 may be identifiedbased on the assessment of the risk of plaque rupture as will bedescribed below in further detail and/or based on input from a user.Also, as shown in FIG. 34, a myocardial segment 912 (of the plurality ofsegments 842) may be identified as having a high probability of lowperfusion due to the rupture of the plaque identified at location 910.

FIGS. 35 and 36 are schematic diagrams showing aspects of a method 920for providing various information relating to assessing plaquevulnerability, myocardial volume risk, and myocardial perfusion risk ina specific patient, according to an exemplary embodiment. The method 920may be implemented in the computer system described above, e.g., thecomputer system used to implement one or more of the steps describedabove and shown in FIG. 3. The method 920 may be performed using one ormore inputs 922, and may include generating one or more models 930 basedon the inputs 922, performing one or more biomechanical analyses 940based on the one or more of the models 930, and providing variousresults based on the models 930 and the biomechanical analyses 940.

The inputs 922 may include medical imaging data 923 of the patient'saorta, coronary arteries (and the branches that extend therefrom), andheart, such as CCTA data (e.g., obtained in step 100 of FIG. 2). Theinputs 922 may also include additional physiological data 924 measuredfrom the patient, such as the patient's brachial blood pressure, heartrate, and/or other measurements (e.g., obtained in step 100 of FIG. 2).The additional physiological data 924 may be obtained noninvasively. Theinputs 922 may be used to generate the models 930 and/or perform thebiomechanical analyses 940 described below.

As noted above, one or more models 930 may be generated based on theinputs 922. For example, the method 920 may include generating ahemodynamic model 932 including computed blood flow and pressureinformation at various locations throughout a three-dimensionalgeometric model of the patient's anatomy. The model of the patient'sanatomy may be created using the medical imaging data 923, e.g., thesolid model 320 of FIG. 8 generated in step 306 of FIG. 3, and/or themesh 380 of FIGS. 17-19 generated in step 312 of FIG. 3, and, in anexemplary embodiment, the hemodynamic model 932 may be the simulatedblood pressure model 50 (FIG. 1), the simulated blood flow model 52(FIG. 1), the cFFR model 54 (FIG. 1), or other simulation produced afterperforming a computational analysis, e.g., as described above inconnection with step 402 of FIG. 3. Solid mechanics models, includingfluid structure interaction models, may be solved with the computationalanalysis with known numerical methods. Properties for the plaque andvessels may be modeled as linear or nonlinear, isotropic or anisotropic.The solution may provide stress and strain of the plaque and theinterface between the plaque and the vessel. In the exemplary embodimentshown in FIG. 36, the hemodynamic model 932 is the cFFR model 54.

The method 920 may include performing a biomechanical analysis 940 usingthe hemodynamic model 932 by computing a pressure 906 (FIG. 33) andshear stress 908 (FIG. 33) acting on a plaque luminal surface due tohemodynamic forces at various physiological states, such as rest,varying levels of exercise or exertion, etc. (step 942). The pressure906 and shear stress 908 may be calculated based on information from thehemodynamic model 932, e.g., blood pressure and flow.

Optionally, the method 920 may also include generating a geometricanalysis model 934 for quantifying vessel deformation fromfour-dimensional imaging data, e.g., imaging data obtained at multiplephases of the cardiac cycle, such as the systolic and diastolic phases.The imaging data may be obtained using various known imaging methods.The geometric analysis model 934 may include information regardingvessel position, deformation, orientation, and size, e.g., due tocardiac motion, at the different phases of the cardiac cycle. Forexample, various types of deformation of the patient's aorta, coronaryarteries (and the branches that extend therefrom), and the plaque, suchas longitudinal lengthening (elongation) or shortening, twisting(torsion), radial expansion or compression, and bending, may besimulated by the geometric analysis model 934.

The method 920 may include performing a biomechanical analysis 940 usingthe geometric analysis model 934 by computing various deformationcharacteristics, such as longitudinal lengthening (elongation) orshortening, twisting (torsion), radial expansion or compression, andbending, etc., of the patient's aorta, coronary arteries (and thebranches that extend therefrom), and the plaque due to cardiac-inducedpulsatile pressure (step 944). These deformation characteristics may becalculated based on information from the geometric analysis model 934,e.g., a change in vessel position, orientation, and size, over multiplephases of the cardiac cycle.

The calculation of the deformation characteristics may be simplified bydetermining centerlines or surface meshes of the modeled geometry (e.g.,the geometry of the patient's aorta, coronary arteries (and the branchesthat extend therefrom), the plaque, etc.). To determine a change in themodeled geometry between different phases, branch ostia, calcifiedlesions, and soft plaque may be used as landmarks. In the regions thathave no landmarks, cross-sectional area profiles along a length of themodeled geometry may be used to identify corresponding locations betweenthe two image frames (to “register” the two image frames). Deformableregistration algorithms based on raw image data may be used to extractthree-dimensional deformation fields. The calculated three-dimensionaldeformation field may then be projected to a curvilinear axis alignedwith the modeled geometry (e.g., the vessel length) to computetangential and normal components of the deformation field. The resultingdifference in modeled geometry (e.g., vessel length), angle of branchseparation, and curvature between systole and diastole may be used todetermine the strain experienced by a vessel.

The method 920 may also include generating a plaque model 936 fordetermining plaque composition and properties from the medical imagingdata 923. For example, the plaque model 936 may include informationregarding density and other material properties of the plaque.

The method 920 may also include generating a vessel wall model 938 forcomputing information about the plaque, the vessel walls, and/or theinterface between the plaque and the vessel walls. For example, thevessel wall model 938 may include information regarding stress andstrain, which may be calculated based on the plaque composition andproperties included in the plaque model 936, the pressure 906 and shearstress 908 calculated in step 942, and/or the deformationcharacteristics calculated in step 944.

The method 920 may include performing a biomechanical analysis 940 usingthe vessel wall model 938 by computing stress (e.g., acute or cumulativestress) on the plaque due to hemodynamic forces and cardiacmotion-induced strain (step 946). For example, the flow-induced force904 (FIG. 33) acting on the plaque may be computed. The stress or forceon the plaque due to hemodynamic forces and cardiac motion-inducedstrain may be calculated based on information from the vessel wall model938, e.g., stress and strain on the plaque.

The method 920 may include determining further information based on oneor more of the models 930 and one or more of the biomechanical analyses940 described above.

A plaque rupture vulnerability index may be calculated (step 950). Theplaque rupture vulnerability index may be calculated, e.g., based ontotal hemodynamic stress, stress frequency, stress direction, and/orplaque strength or other properties. For example, a region surrounding aplaque of interest may be isolated from the three-dimensional model 930of the plaque, such as the plaque model 936. The strength of the plaquemay be determined from the material properties provided in the plaquemodel 936. A hemodynamic and tissue stress on the plaque of interest,due to pulsatile pressure, flow, and heart motion, may be calculatedunder simulated baseline and exercise (or exertion) conditions by usingthe hemodynamic stresses and motion-induced strains previously computedin step 946. The vulnerability of the plaque may be assessed based onthe ratio of plaque stress to plaque strength.

A myocardial volume risk index (MVRI) may also be calculated (step 952).The MVRI may be defined as a percentage of the total myocardial volumeaffected by a plaque rupture and occlusion (closure or obstruction) of avessel at a given location in the arterial tree. The MVRI may becalculated based on the portion of the myocardium supplied by thevessels downstream of the given plaque, which may take into account thesize of the plaque with respect to the size of the downstream vesselsand the probability that the plaque may flow into different vesselsbased on the three-dimensional hemodynamic solution.

The myocardium may be modeled and divided into segments 842 supplied byeach vessel in the hemodynamic simulation (e.g., as described inconnection with steps 835 and 840 of FIG. 30). The geometric model maybe modified to include a next generation of branches 857 in the coronarytree (e.g., as described in connection with step 855 of FIG. 30), andthe myocardium may be further segmented (e.g., as described inconnection with step 860 of FIG. 30). Additional branches 857 may becreated in the subsegments 862, and the subsegments 862 may be furthersegmented into smaller segments 867 (e.g., as described in connectionwith step 865 of FIG. 30). Physiologic relationships, as previouslydescribed, may be used to relate the size of a vessel to a proportionalamount of myocardium supplied.

Potential paths for a ruptured plaque to follow may be determined. Thehemodynamic solution may be used to determine a percent chance that aplaque fragment or embolus may flow into different downstream vessels.

The size of the ruptured plaque may be compared with the size of thedownstream vessels to determine where the plaque may eventually createan impediment to flow. This information may be combined with thevulnerability index to provide a probability map of the volume of themyocardium that may potentially be affected by the ruptured plaque. TheMVRI may be assigned to each potential affected segment. FIG. 34 showsan example of a segment 912 where the vulnerable plaque at location 910in a distal vessel has a high probability of affecting a small area ofthe myocardium.

A myocardial perfusion risk index (MPRI) may also be calculated (step954). The MPRI may be defined as a percentage of the total myocardialblood flow affected by a plaque rupture and occlusion of a vessel at agiven location in the arterial tree. For example, a rupture of plaque ina distal portion of the LAD artery would yield a lower MVRI and a lowerMPRI than a rupture of plaque in a proximal portion of the LAD artery.These indices may differ, however, if a portion of the myocardial volumeaffected by a vulnerable plaque in a feeding vessel is not viable (e.g.,due to scar tissue that may form subsequent to myocardial infarction).Thus, the MPRI indicates a potential loss of perfusion to the myocardiumsegments, rather than the volume affected as indicated by the MVRI. Theperfusion rate to each segment 842, 862, or 867 of FIG. 31 may becalculated, and the loss of perfusion may be calculated based on thevulnerability index, the hemodynamic solution, and the sizes of theplaque and vessels.

As a result, plaque stress due to pulsatile blood pressure, pulsatileblood flow, pulsatile blood shear stress, and/or pulsatile cardiacmotion may be calculated, and plaque strength may be estimated based onmedical imaging data, and indices relating to plaque vulnerability,myocardial volume risk, and myocardial perfusion risk may be quantified.

VIII. Other Applications

The embodiments described above are associated with assessinginformation about coronary blood flow in a patient. Alternatively, theembodiments may also be adapted to blood flow in other areas of thebody, such as, but not limited to, the carotid, peripheral, abdominal,renal, femoral, popliteal, and cerebral arteries.

A. Modeling Intracranial and Extracranial Blood Flow

Embodiments relating to the cerebral arteries will now be described.Numerous diseases may influence or be affected by blood flow andpressure in the extracranial or intracranial arteries. Atheroscleroticdisease in the extracranial, e.g. carotid and vertebral, arteries mayrestrict blood flow to the brain. A severe manifestation ofatherosclerotic disease may lead to a transient ischemic attack or anischemic stroke. Aneurysmal disease in the intracranial or extracranialarteries may pose a risk of embolization leading to ischemic stroke oraneurysm rupture leading to hemorrhagic stroke. Other conditions such ashead trauma, hypertension, head and neck cancer, arteriovenousmalformations, orthostatic intolerance, etc., may also affect cerebralblood flow. Furthermore, reductions in cerebral blood flow may inducesymptoms such as syncope or impact chronic neurologic disorders such asdementia subsequent to Alzheimer's or Parkinson's disease.

Patients with known or suspected extracranial or intracranial arterialdisease may typically receive one or more of the following noninvasivediagnostic tests: US, MRI, CT, PET. These tests, however, may not beable to efficiently provide anatomic and physiologic data forextracranial and intracranial arteries for most patients.

FIG. 37 is a diagram of cerebral arteries, including intracranial(within the cranium) and extracranial (outside the cranium) arteries.The methods for determining information regarding patient-specificintracranial and extracranial blood flow may be generally similar to themethods for determining information regarding patient-specific coronaryblood flow as described above.

FIG. 38 is a schematic diagram showing aspects of a method 1000 forproviding various information relating to intracranial and extracranialblood flow in a specific patient. The method 1000 may be implemented ina computer system, e.g., similar to the computer system used toimplement one or more of the steps described above and shown in FIG. 3.The method 1000 may be performed using one or more inputs 1010, and mayinclude generating one or more models 1020 based on the inputs 1010,assigning one or more conditions 1030 based on the inputs 1010 and/orthe models 1020, and deriving one or more solutions 1040 based on themodels 1020 and the conditions 1030.

The inputs 1010 may include medical imaging data 1011 of the patient'sintracranial and extracranial arteries, e.g., the patient's aorta,carotid arteries (shown in FIG. 37), vertebral arteries (shown in FIG.37), and brain, such as CCTA data (e.g., obtained in a similar manner asdescribed above in connection with step 100 of FIG. 2). The inputs 1010may also include a measurement 1012 of the patient's brachial bloodpressure, carotid blood pressure (e.g., using tonometry), and/or othermeasurements (e.g., obtained in a similar manner as described above inconnection with step 100 of FIG. 2). The measurements 1012 may beobtained noninvasively. The inputs 1010 may be used to generate themodel(s) 1020 and/or determine the condition(s) 1030 described below.

As noted above, one or more models 1020 may be generated based on theinputs 1010. For example, the method 1000 may include generating one ormore patient-specific three-dimensional geometric models of thepatient's intracranial and extracranial arteries based on the imagingdata 1011 (step 1021). The three-dimensional geometric model 1021 may begenerated using similar methods as described above for generating thesolid model 320 of FIG. 8 and the mesh 380 of FIGS. 17-19. For example,similar steps as steps 306 and 312 of FIG. 3 may be used to generate athree-dimensional solid model and mesh representing the patient'sintracranial and extracranial arteries.

Referring back to FIG. 38, the method 1000 may also include generatingone or more physics-based blood flow models (step 1022). For example,the blood flow model may be a model that represents the flow through thepatient-specific geometric model generated in step 1021, heart andaortic circulation, distal intracranial and extracranial circulation,etc. The blood flow model may include reduced order models as describedabove in connection with step 310 of FIG. 3, e.g., the lumped parametermodels or distributed (one-dimensional wave propagation) models, etc.,at the inflow boundaries and/or outflow boundaries of thethree-dimensional geometric model 1021. Alternatively, the inflowboundaries and/or outflow boundaries may be assigned respectiveprescribed values or field for velocity, flow rate, pressure, or othercharacteristic, etc. As another alternative the inflow boundary may becoupled to a heart model, e.g., including the aortic arch. Theparameters for the inflow and/or outflow boundaries may be adjusted tomatch measured or selected physiological conditions including, butlimited to, cardiac output and blood pressure.

As noted above, one or more conditions 1030 may be determined based onthe inputs 1010 and/or the models 1020. The conditions 1030 include theparameters calculated for the boundary conditions determined in step1022 (and step 310 of FIG. 3). For example, the method 1000 may includedetermining a condition by calculating a patient-specific brain or headvolume based on the imaging data 1011 (e.g., obtained in a similarmanner as described above in connection with step 240 of FIG. 3) (step1031).

The method 1000 may include determining a condition by calculating,using the brain or head volume calculated in step 1031, a restingcerebral blood flow Q based on the relationship Q=Q_(o)M^(α), where α isa preset scaling exponent, M is the brain mass determined from the brainor head volume, and Q^(o) is a preset constant (e.g., similar to thephysiological relationship described above in connection withdetermining the lumped parameter model in step 310 of FIG. 3) (step1032). Alternatively, the relationship may have the form Q∝Q_(o)M^(α),as described above in connection with determining the lumped parametermodel in step 310 of FIG. 3.

The method 1000 may also include determining a condition by calculating,using the resulting coronary flow calculated in step 1032 and thepatient's measured blood pressure 1012, a total resting cerebralresistance (e.g., similar to the methods described above in connectionwith determining the lumped parameter model in step 310 of FIG. 3) (step1033). For example, the total cerebral blood flow Q at the outflowboundaries of the three-dimensional geometric model 1021 under baseline(resting) conditions determined in step 1032 and the measured bloodpressure 1012 may be used to determine a total resistance R at theoutflow boundaries based on a preset, experimentally-derived equation.Resistance, capacitance, inductance, and other variables associated withvarious electrical components used in lumped parameter models may beincorporated into the boundary conditions (e.g., as described above inconnection with determining the lumped parameter model in step 310 ofFIG. 3).

The method 1000 may also include determining a condition by calculating,using the total resting cerebral resistance calculated in step 1033 andthe models 1020, individual resistances for the individual intracranialand extracranial arteries (step 1034). For example, similar to themethods described above in connection with step 310 of FIG. 3, the totalresting cerebral resistance R calculated in step 1033 may be distributedto the individual intracranial and extracranial arteries based on thesizes (e.g., determined from the geometric model generated in step 1021)of the distal ends of the individual intracranial and extracranialarteries, and based on the relationship R=R_(o)d^(β), where R is theresistance to flow at a particular distal end, and R_(o) is a presetconstant, d is the size (e.g., diameter of that distal end), and β is apreset power law exponent, as described above in connection withdetermining the lumped parameter model in step 310 of FIG. 3.

Referring back to FIG. 38, the method 1000 may include adjusting theboundary conditions based on one or more physical conditions of thepatient (step 1035). For example, the parameters determined in steps1031-1034 may be modified based on whether the solution 1040 is intendedto simulate rest, varying levels of stress, varying levels ofbaroreceptor response or other autonomic feedback control, varyinglevels of hyperemia, varying levels of exercise, exertion, hypertension,or hypotension, different medications, postural change, and/or otherconditions. The parameters (e.g., the parameters relating to theboundary conditions at the outflow boundaries) may also be adjustedbased on a vasodilatory capacity of the intracranial and extracranialarteries (the ability of the blood vessels to widen), e.g., due tomicrovascular dysfunction or endothelial health.

Based on the inputs 1010, the models 1020, and the conditions 1030, acomputational analysis may be performed, e.g., as described above inconnection with step 402 of FIG. 3, to determine the solution 1040 thatincludes information about the patient's coronary blood flow under thephysical conditions selected in step 1035 (step 1041). Examples ofinformation that may be provided from the solution 1040 may be similarto the examples provided above in connection with FIGS. 1 and 21-24,e.g., a simulated blood pressure model, a simulated blood flow model,etc. The results may also be used to determine, e.g., flow rate, totalbrain flow, vessel wall shear stress, traction or shear force acting onvessel walls or atherosclerotic plaque or aneurysm, particle/bloodresidence time, vessel wall movement, blood shear rate, etc. Theseresults may also be used to analyze where emboli leaving from a specificregion in the vascular system may most likely travel due to bloodcirculation.

The computer system may allow the user to simulate various changes ingeometry. For example, the models 1020, e.g., the patient-specificgeometric model generated in step 1021 may be modified to predict theeffect of occluding an artery (e.g., an acute occlusion). In somesurgical procedures, such as when removing cancerous tumors, one or moreextracranial arteries may be damaged or removed. Thus, thepatient-specific geometric model generated in step 1021 may also bemodified to simulate the effect of preventing blood flow to one or moreof the extracranial arteries in order to predict the potential forcollateral pathways for supplying adequate blood flow for the patient.

The computer system may allow the user to simulate the results ofvarious treatment options, such as interventional or surgical repair,e.g., of an acute occlusion. The simulations may be performed morequickly by replacing the three-dimensional solid model or meshrepresenting the intracranial and extracranial arteries, as describedabove, with reduced order models, as described above in connection withFIGS. 27 and 28. As a result, the reduced order models, such asone-dimensional or lumped parameter models, may more efficiently andrapidly solve for blood flow and pressure in a patient-specific modeland display the results of solutions.

A response to vasodilatory stimuli by a specific patient may bepredicted based on hemodynamic information for the patient at rest orbased on population-based data for different disease states. Forexample, in a baseline (resting) simulation is run (e.g., as describedabove in step 1041) with flow distribution assigned based on power lawsand brain mass (e.g., as described above in connection with step 1032).The resistance values (e.g., determined in steps 1033 and 1034) may beadjusted to allow adequate perfusion. Alternatively, data from patientpopulations with such factors as diabetes, medications, and past cardiacevents are used to assign different resistances. The adjustment inresistance under resting conditions, alone or in combination withhemodynamic information (e.g., wall shear stress or a relationship offlow and vessel size), may be used to determine a remaining capacity fordistal cerebral vessels to dilate. Patients requiring resistancereductions to meet resting flow requirements or patients with a highflow to vessel size ratio may have a diminished capacity to furtherdilate their vessels under physiologic stress.

Flow rates and pressure gradients across individual segments of thecerebral arteries (e.g., as determined in step 1041) may be used tocompute a cerebral arterial resistance. The cerebral arterial resistancemay be calculated as an equivalent resistance of the portions of theextracranial and intracranial arteries included in the patient-specificgeometric model generated from medical imaging data (e.g., generated instep 1021). The cerebral arterial resistance may have clinicalsignificance in explaining why patients with diffuse atherosclerosis inextracranial and/or intracranial arteries may exhibit symptoms ofsyncope (temporary loss of consciousness or posture, e.g., fainting) orischemia (restriction in blood supply).

Also, the flow per unit of brain tissue volume (or mass) under baselineor altered physiologic conditions may be calculated, e.g., based on theflow information determined in step 1041 and the brain tissue volume ormass calculated in step 1031. This calculation may be useful inunderstanding the impact of reductions in blood flow on chronicneurological disorders. This calculation may also be useful in selectingor refining medical therapies, e.g., dosage of antihypertensives.Additional results may include quantifying the effects of trauma,concussion, external physiologic stresses, excess G-forces,weightlessness, space flight, deep sea decompression (e.g., the bends),etc.

The combined patient-specific anatomic (geometric) and physiologic(physics-based) model may be used to determine the effect of differentmedications or lifestyle changes (e.g., cessation of smoking, changes indiet, or increased physical activity) that alters heart rate, strokevolume, blood pressure, or cerebral microcirculatory function oncerebral artery blood flow. The combined model may also be used todetermine the effect on cerebral artery blood flow of alternate formsand/or varying levels of physical activity or risk of exposure topotential extrinsic force, e.g., when playing football, during spaceflight, when scuba diving, during airplane flights, etc. Suchinformation may be used to identify the types and level of physicalactivity that may be safe and efficacious for a specific patient. Thecombined model may also be used to predict a potential benefit ofpercutaneous interventions on cerebral artery blood flow in order toselect the optimal interventional strategy, and/or to predict apotential benefit of carotid endarterectomy orexternal-carotid-to-internal-carotid bypass grafting on cerebral arteryblood flow in order to select the optimal surgical strategy.

The combined model may also be used to illustrate potential deleteriouseffects of an increase in the burden of arterial disease on cerebralartery blood flow and to predict, using mechanistic or phenomenologicaldisease progression models or empirical data, when advancing disease mayresult in a compromise of blood flow to the brain. Such information mayenable the determination of a “warranty period” in which a patientobserved to be initially free from hemodynamically significant diseaseusing noninvasive imaging may not be expected to require medical,interventional, or surgical therapy, or alternatively, the rate at whichprogression might occur if adverse factors are continued.

The combined model may also be used to illustrate potential beneficialeffects on cerebral artery blood flow resulting from a decrease in theburden of disease and to predict, using mechanistic or phenomenologicaldisease progression models or empirical data, when regression of diseasemay result in increased blood flow to the brain. Such information may beused to guide medical management programs including, but not limited to,changes in diet, increased physical activity, prescription of statins orother medications, etc.

The combined model may also be used to predict the effect of occludingan artery. In some surgical procedures, such as the removal of canceroustumors, some extracranial arteries may be damaged or removed. Simulatingthe effect of preventing blood flow to one of the extracranial arteriesmay allow prediction of the potential for collateral pathways to supplyadequate blood flow for a specific patient.

i. Assessing Cerebral Perfusion

Other results may be calculated. For example, the computational analysismay provide results that quantify cerebral perfusion (blood flow throughthe cerebrum). Quantifying cerebral perfusion may assist in identifyingareas of reduced cerebral blood flow.

FIG. 39 shows a schematic diagram relating to a method 1050 forproviding various information relating to cerebral perfusion in aspecific patient, according to an exemplary embodiment. The method 1050may be implemented in the computer system described above, e.g., similarto the computer system used to implement one or more of the stepsdescribed above and shown in FIG. 3.

The method 1050 may be performed using one or more inputs 1052. Theinputs 1052 may include medical imaging data 1053 of the patient'sintracranial and extracranial arteries, e.g., the patient's aorta,carotid arteries (shown in FIG. 37), vertebral arteries (shown in FIG.37), and brain, such as CCTA data (e.g., obtained in a similar manner asdescribed above in connection with step 100 of FIG. 2). The inputs 1052may also include additional physiological data 1054 measured from thepatient, such as the patient's brachial blood pressure, heart rate,and/or other measurements (e.g., obtained in a similar manner asdescribed above in connection with step 100 of FIG. 2). The additionalphysiological data 1054 may be obtained noninvasively. The inputs 1052may be used to perform the steps described below.

A three-dimensional geometric model of the patient's brain tissue may becreated based on the imaging data 1053 (step 1060) and the geometricmodel may be divided into segments or volumes (step 1062) (e.g., in asimilar manner as described above in connection with FIGS. 29-32). Thesizes and locations of the individual segments may be determined basedon the locations of the outflow boundaries of the intracranial andextracranial arteries, the sizes of the blood vessels in or connected tothe respective segments (e.g., the neighboring blood vessels), etc. Thedivision of the geometric model into segments may be performed usingvarious known methods, such as a fast marching method, a generalizedfast marching method, a level set method, a diffusion equation,equations governing flow through a porous media, etc.

The three-dimensional geometric model may also include a portion of thepatient's intracranial and extracranial arteries, which may be modeledbased on the imaging data 1053 (step 1064). For example, in steps 1062and 1064, a three-dimensional geometric model may be created thatincludes the brain tissue and the intracranial and extracranialarteries.

A computational analysis may be performed, e.g., as described above inconnection with step 402 of FIG. 3, to determine a solution thatincludes information about the patient's cerebral blood flow under aphysical condition determined by the user (step 1066). For example, thephysical condition may include rest, varying levels of stress, varyinglevels of baroreceptor response or other autonomic feedback control,varying levels of hyperemia, varying levels of exercise or exertion,different medications, postural change, and/or other conditions. Thesolution may provide information, such as blood flow and pressure, atvarious locations in the anatomy of the patient modeled in step 1064 andunder the specified physical condition. The computational analysis maybe performed using boundary conditions at the outflow boundaries derivedfrom lumped parameter or one-dimensional models. The one-dimensionalmodels may be generated to fill the segments of the brain tissue asdescribed below in connection with FIG. 40.

Based on the blood flow information determined in step 1066, theperfusion of blood flow into the respective segments of the braincreated in step 1062 may be calculated (step 1068). For example, theperfusion may be calculated by dividing the flow from each outlet of theoutflow boundaries by the volume of the segmented brain to which theoutlet perfuses.

The perfusion for the respective segments of the brain determined instep 1068 may be displayed on the geometric model of the brain generatedin step 1060 or 1062 (step 1070). For example, the segments of the brainshown in the geometric model created in step 1060 may be illustratedwith a different shade or color to indicate the perfusion of blood flowinto the respective segments.

FIG. 40 shows another schematic diagram relating to a method 1100 forproviding various information relating to cerebral perfusion in aspecific patient, according to an exemplary embodiment. The method 1100may be implemented in the computer system described above, e.g., similarto the computer system used to implement one or more of the stepsdescribed above and shown in FIG. 3.

The method 1100 may be performed using one or more inputs 1102, whichmay include medical imaging data 1103 of the patient's aorta, carotidarteries (shown in FIG. 37), vertebral arteries (shown in FIG. 37), andbrain, such as CCTA data (e.g., obtained in a similar manner asdescribed above in connection with step 100 of FIG. 2). The inputs 1102may be used to perform the steps described below.

A three-dimensional geometric model of the patient's brain tissue may becreated based on the imaging data 1103 (step 1110). The model may alsoinclude a portion of the patient's aorta, carotid arteries (shown inFIG. 37), and vertebral arteries (shown in FIG. 37), which may also becreated based on the imaging data 1103. For example, as described above,a three-dimensional geometric model may be created that includes thebrain tissue and the intracranial and extracranial arteries. Step 1110may include steps 1060 and 1064 of FIG. 39 described above.

The geometric brain tissue model created in step 1110 may be dividedinto volumes or segments (step 1112). Step 1112 may include step 1062 ofFIG. 39 described above. The geometric brain tissue model may also befurther modified to include a next generation of branches in thecerebral tree (step 1118) (e.g., in a similar manner as described abovein connection with FIGS. 29-32). The location and size of the branchesmay be determined based on centerlines for the intracranial andextracranial arteries. The centerlines may be determined, e.g., based onthe imaging data 1103 (step 1114). An algorithm may also be used todetermine the location and size of the branches based on morphometricmodels (models used to predict vessel location and size downstream ofthe known outlets at the outflow boundaries) and/or physiologicbranching laws related to vessel size (step 1116). The morphometricmodel may be augmented to the downstream ends of the intracranial andextracranial arteries included in the geometric model, and provided onthe outer layer of brain tissue or contained within the geometric modelof the brain tissue.

The brain may be further segmented based on the branches created in step1118 (step 1120) (e.g., in a similar manner as described above inconnection with FIGS. 29-32). Additional branches may be created in thesubsegments, and the subsegments may be further segmented into smallersegments (step 1122) (e.g., in a similar manner as described above inconnection with FIGS. 29-32). The steps of creating branches andsub-segmenting the volumes may be repeated until a desired resolution ofvolume size and/or branch size is obtained. The geometric model, whichhas been augmented to include new branches in steps 1118 and 1122, maythen be used to compute cerebral blood flow and cerebral perfusion intothe subsegments, such as the subsegments generated in step 1122.

Accordingly, the augmented model may be used to perform thecomputational analysis described above. The results of the computationalanalysis may provide information relating to the blood flow from thepatient-specific cerebral artery model, into the generated morphometricmodel (including the branches generated in steps 1118 and 1122), whichmay extend into each of the perfusion subsegments generated in step1122.

FIG. 41 shows another schematic diagram relating to a method 1150 forproviding various information relating to cerebral perfusion in aspecific patient, according to an exemplary embodiment. The method 1150may be implemented in the computer system described above, e.g., thecomputer system used to implement one or more of the steps describedabove and shown in FIG. 3.

The method 1150 may be performed using one or more inputs 1152. Theinputs 1152 may include medical imaging data 1153 of the patient'saorta, carotid arteries (shown in FIG. 37), vertebral arteries (shown inFIG. 37), and brain, such as CCTA data (e.g., obtained in a similarmanner as described above in connection with step 100 of FIG. 2). Theinputs 1152 may also include additional physiological data 1154 measuredfrom the patient, such as the patient's brachial blood pressure, heartrate, and/or other measurements (e.g., obtained in step 100 of FIG. 2).The additional physiological data 1154 may be obtained noninvasively.The inputs 1152 may further include brain perfusion data 1155 measuredfrom the patient (e.g., using CT, PET, SPECT, MRI, etc.). The inputs1152 may be used to perform the steps described below.

A three-dimensional geometric model of the patient's intracranial andextracranial arteries may be created based on the imaging data 1153(step 1160). Step 1160 may be similar to step 1064 of FIG. 39 describedabove.

A computational analysis may be performed, e.g., as described above inconnection with step 402 of FIG. 3, to determine a solution thatincludes information about the patient's cerebral blood flow under aphysical condition determined by the user (step 1162). For example, thephysical condition may include rest, varying levels of stress, varyinglevels of baroreceptor response or other autonomic feedback control,varying levels of hyperemia, varying levels of exercise or exertion,different medications, postural change, and/or other conditions. Thesolution may provide information, such as blood flow and pressure, atvarious locations in the anatomy of the patient modeled in step 1160 andunder the specified physical condition. Step 1162 may be similar to step1066 of FIG. 39 described above.

Also, a three-dimensional geometric model of the patient's brain tissuemay be created based on the imaging data 1153 (step 1164). For example,in steps 1160 and 1164, a three-dimensional geometric model may becreated that includes the brain tissue and the intracranial andextracranial arteries. Step 1164 may be similar to step 1060 of FIG. 39described above.

The geometric model may be divided into segments or subvolumes (step1166). Step 1166 may be similar to step 1062 of FIG. 39 described above.

Based on the blood flow information determined in step 1162, theperfusion of blood flow into the respective segments of the brain tissuecreated in step 1166 may be calculated (step 1168). Step 1168 may besimilar to step 1068 of FIG. 39 described above.

The calculated perfusion for the respective segments of the brain tissuemay be displayed on the geometric model of the brain tissue generated instep 1164 or 1166 (step 1170). Step 1170 may be similar to step 1070 ofFIG. 39 described above.

The simulated perfusion data mapped onto the three-dimensional geometricmodel of the brain tissue in step 1170 may be compared with the measuredcerebral perfusion data 1155 (step 1172). The comparison may indicatethe differences in the simulated and measured perfusion data usingvarious colors and/or shades on the three-dimensional representation ofthe brain tissue.

The boundary conditions at the outlets of the three-dimensionalgeometric model created in step 1160 may be adjusted to decrease theerror between the simulated and measured perfusion data (step 1174). Forexample, in order to reduce the error, the boundary conditions may beadjusted so that the prescribed resistance to flow of the vesselsfeeding a region (e.g., the segments created in step 1166) where thesimulated perfusion is lower than the measured perfusion may be reduced.Other parameters of the boundary conditions may be adjusted.Alternatively, the branching structure of the model may be modified. Forexample, the geometric model created in step 1160 may be augmented asdescribed above in connection with FIG. 40 to create the morphometricmodel. The parameters of the boundary conditions and/or morphometricmodels may be adjusted empirically or systematically using a parameterestimation or data assimilation method, such as the method described inU.S. Patent Application Publication No. 2010/0017171, which is entitled“Method for Tuning Patient-Specific Cardiovascular Simulations,” orother methods.

Steps 1162, 1168, 1170, 1172, 1174, and/or other steps of FIG. 41 may berepeated, e.g., until the error between the simulated and measuredperfusion data is below a predetermined threshold. As a result, thecomputational analysis may be performed using a model that relatesanatomical information, cerebral blood flow information, and cerebralperfusion information. Such a model may be useful for diagnosticpurposes and for predicting the benefits of medical, interventional, orsurgical therapies.

As a result, extracranial and intracranial arterial blood flow andcerebral perfusion under baseline conditions or altered physiologicstates may be computed. Cerebral perfusion data may be used incombination with simulated cerebral perfusion results to adjust theboundary conditions of the intracranial artery blood flow computationsuntil the simulated cerebral perfusion results match the measuredcerebral perfusion data within a given tolerance. Thus, more accuratepatient-specific extracranial and intracranial arterial blood flowcomputations may be provided and physicians may predict cerebral arteryblood flow and cerebral perfusion when measured data may be unavailable,e.g., certain physical conditions such as exercise, exertion, posturalchanges, or simulated treatments. The patient-specific three-dimensionalmodel of the brain may be divided into perfusion segments or subvolumes,and it may be determined whether a patient is receiving adequate minimumperfusion to various regions of the brain.

A patient-specific three-dimensional geometric model of the intracranialarteries may be generated from medical imaging data and combined with amorphometric model of a portion of the remaining intracranial arterialtree represented by perfusion segments or subvolumes (e.g., as describedabove in connection with FIG. 40) to form an augmented model. Thepercentage of the total brain volume (or mass) downstream of a given,e.g. diseased, location in the augmented model may be calculated. Also,the percentage of the total cerebral blood flow at a given, e.g.diseased, location in the augmented model may be calculated. Inaddition, deficits noted in functional imaging studies (e.g., functionalmagnetic resonance imaging (fMRI)), perfusion CT or MRI, may then betraced to disease in the feeding vessels, anatomic variants, impairedautoregulatory mechanisms, hypotension, or other conditions, which maybe useful for patients with ischemic stroke, syncope, orthostaticintolerance, trauma, or chronic neurologic disorders.

ii. Assessing Plague Vulnerability

The computational analysis may also provide results that quantifypatient-specific biomechanical forces acting on plaque that may build upin the patient's intracranial and extracranial arteries, e.g., carotidatherosclerotic plaque. The biomechanical forces may be caused bypulsatile pressure, flow, and neck motion.

FIG. 42 is a schematic diagram showing aspects of a method 1200 forproviding various information relating to assessing plaquevulnerability, cerebral volume risk, and cerebral perfusion risk in aspecific patient, according to an exemplary embodiment. The method 1200may be implemented in the computer system described above, e.g., similarto the computer system used to implement one or more of the stepsdescribed above and shown in FIG. 3. The method 1200 may be performedusing one or more inputs 1202, and may include generating one or moremodels 1210 based on the inputs 1202, performing one or morebiomechanical analyses 1220 based on the one or more of the models 1210,and providing various results based on the models 1210 and thebiomechanical analyses 1220.

The inputs 1202 may include medical imaging data 1203 of the patient'sintracranial and extracranial arteries, e.g., the patient's aorta,carotid arteries (shown in FIG. 37), vertebral arteries (shown in FIG.37), and brain, such as CCTA data (e.g., obtained in a similar manner asdescribed above in connection with step 100 of FIG. 2). The inputs 1202may also include additional physiological data 1204 measured from thepatient, such as the patient's brachial blood pressure, heart rate,and/or other measurements (e.g., obtained in a similar manner asdescribed above in connection with step 100 of FIG. 2). The additionalphysiological data 1204 may be obtained noninvasively. The inputs 1202may be used to generate the models 1210 and/or perform the biomechanicalanalyses 1220 described below.

As noted above, one or more models 1210 may be generated based on theinputs 1202. For example, the method 1200 may include generating ahemodynamic model 1212 including computed blood flow and pressureinformation at various locations throughout a three-dimensionalgeometric model of the patient's anatomy. The model of the patient'sanatomy may be created using the medical imaging data 1203, and, in anexemplary embodiment, the hemodynamic model 1212 may be a simulatedblood pressure model, the simulated blood flow model, or othersimulation produced after performing a computational analysis, e.g., asdescribed above in connection with step 402 of FIG. 3. Solid mechanicsmodels, including fluid structure interaction models, may be solved withthe computational analysis with known numerical methods. Properties forthe plaque and vessels may be modeled as linear or nonlinear, isotropicor anisotropic. The solution may provide stress and strain of the plaqueand the interface between the plaque and the vessel. The steps forgenerating the hemodynamic model 1212 may be similar to the steps forgenerating the hemodynamic model 932 of FIG. 35 described above.

The method 1200 may include performing a biomechanical analysis 1220using the hemodynamic model 1212 by computing a pressure and shearstress acting on a plaque luminal surface due to hemodynamic forces atvarious physiological states, such as rest, varying levels of exerciseor exertion, etc. (step 1222). The pressure and shear stress may becalculated based on information from the hemodynamic model 1212, e.g.,blood pressure and flow. Step 1222 may be similar to step 942 of FIG. 35described above.

Optionally, the method 1200 may also include generating a geometricanalysis model for quantifying vessel deformation from four-dimensionalimaging data, e.g., imaging data obtained at multiple phases of thecardiac cycle, such as the systolic and diastolic phases, in a similarmanner as described above for the geometric analysis model 934 of FIG.35. The method 1200 may also include performing a biomechanical analysis1220 using the geometric analysis model by computing various deformationcharacteristics, such as longitudinal lengthening (elongation) orshortening, twisting (torsion), radial expansion or compression, andbending, etc., of the patient's intracranial and extracranial arteriesand the plaque due to cardiac-induced pulsatile pressure, in a similarmanner as described above for step 944 of FIG. 35.

The method 1200 may also include generating a plaque model 1214 fordetermining plaque composition and properties from the medical imagingdata 1203. For example, the plaque model 1214 may include informationregarding density and other material properties of the plaque.

The method 1200 may also include generating a vessel wall model 1216 forcomputing information about the plaque, the vessel walls, and/or theinterface between the plaque and the vessel walls. For example, thevessel wall model 1216 may include information regarding stress andstrain, which may be calculated based on the plaque composition andproperties included in the plaque model 1214 and the pressure and shearstress calculated in step 1220. Optionally, stress and strain may alsobe calculated using calculated deformation characteristics, as describedabove. The steps for generating the plaque model 1214 and/or the vesselwall model 1216 may be similar to the steps for generating the plaquemodel 936 and/or the vessel wall model 938 of FIG. 35 described above.

The method 1200 may include performing a biomechanical analysis 1220using the vessel wall model 1216 by computing stress (e.g., acute orcumulative stress) on the plaque due to hemodynamic forces and neckmovement-induced strain (step 1224). For example, the flow-induced force904 (FIG. 33) acting on the plaque may be computed. The stress or forceon the plaque due to hemodynamic forces and neck movement-induced strainmay be calculated based on information from the vessel wall model 1216,e.g., stress and strain on the plaque. Step 1224 may be similar to step946 of FIG. 35 described above.

The method 1200 may include determining further information based on oneor more of the models 1210 and one or more of the biomechanical analyses1220 described above.

A plaque rupture vulnerability index may be calculated (step 1230). Theplaque rupture vulnerability index may be calculated, e.g., based onhemodynamic stress, stress frequency, stress direction, and/or plaquestrength or other properties. For example, a region surrounding a plaqueof interest may be isolated from the three-dimensional model 1210 of theplaque, such as the plaque model 1214. The strength of the plaque may bedetermined from the material properties provided in the plaque model1214. A hemodynamic and tissue stress on the plaque of interest, due topulsatile pressure, flow, and neck motion, may be calculated undersimulated baseline and exercise (or exertion) conditions by using thehemodynamic stresses and motion-induced strains previously computed instep 1224. The vulnerability of the plaque may be assessed based on theratio of plaque stress to plaque strength. Step 1230 may be similar tostep 950 of FIG. 35 described above. For example, the plaque rupturevulnerability index may be calculated for a plaque located in anextracranial artery for stroke assessment.

A cerebral volume risk index (CVRI) may also be calculated (step 1232).The CVRI may be defined as a percentage of the total brain volumeaffected by a plaque rupture or embolization and occlusion (closure orobstruction) of a vessel at a given location in the arterial tree. TheCVRI may be calculated based on the portion of the brain supplied by thevessels downstream of the given plaque, which may take into account thesize of the plaque with respect to the size of the downstream vesselsand the probability that the plaque may flow into different vesselsbased on the three-dimensional hemodynamic solution. The CVRI may beassessed in diseased states, or before or after an intervention. Step1232 may be similar to step 952 of FIG. 35 described above.

The brain tissue may be modeled and divided into segments supplied byeach vessel in the hemodynamic simulation (e.g., as described inconnection with steps 1110 and 1112 of FIG. 40). The geometric model maybe modified to include a next generation of branches in the cerebraltree (e.g., as described in connection with step 1118 of FIG. 40), andthe brain tissue may be further segmented (e.g., as described inconnection with step 1120 of FIG. 40). Additional branches may becreated in the subsegments, and the subsegments may be further segmentedinto smaller segments (e.g., as described in connection with step 1122of FIG. 40). Physiologic relationships, as previously described, may beused to relate the size of a vessel to a proportional amount of braintissue supplied.

Potential paths for a ruptured plaque to follow may be determined. Thehemodynamic solution may be used to determine a percent chance that aplaque fragment or embolus may flow into different downstream vessels.

The size of the ruptured plaque may be compared with the size of thedownstream vessels to determine where the plaque may eventually createan impediment to flow. This information may be combined with thevulnerability index to provide a probability map of the volume of thebrain tissue that may potentially be affected by the ruptured plaque.The CVRI may be assigned to each potential affected segment.

A cerebral perfusion risk index (CPRI) may also be calculated (step1234). The CPRI may be defined as a percentage of the total cerebralblood flow affected by a plaque rupture and occlusion of a vessel at agiven location in the arterial tree. The CPRI indicates a potential lossof perfusion to the brain tissue segments, rather than the volumeaffected as indicated by the CVRI. For example, the effect of a ruptureor embolization of a carotid artery plaque may vary depending on thegeometry of the patient's circle of Willis (shown in FIG. 37) and mayyield different CVRI and CPRI values due to these differences inanatomy. The perfusion rate to each segment of the brain tissue may becalculated, and the loss of perfusion may be calculated based on thevulnerability index, the hemodynamic solution, and the sizes of theplaque and vessels. The CPRI may be assessed in diseased states, orbefore or after an intervention. Step 1234 may be similar to step 954 ofFIG. 35 described above.

As a result, biomechanical forces acting on carotid atheroscleroticplaques resulting from pulsatile pressure, pulsatile blood flow, and/oroptionally neck motion may be assessed. The total stress that the plaqueexperiences resulting from the pulsatile pressure, pulsatile blood flow,and/or optionally neck motion may be quantified. The solution may takeinto account multiple sources of patient-specific hemodynamic stressacting on the plaque or on the interface between the plaque and thevessel wall. Also, plaque strength may be estimated based on medicalimaging data, and indices relating to plaque vulnerability, cerebralvolume risk, and cerebral perfusion risk may be quantified.

By determining anatomic and physiologic data for extracranial andintracranial arteries as described below, changes in blood flow at thearterial or organ level for a specific patient at various physicalconditions may be predicted. Further, other information may be provided,such as a risk of transient ischemic attack, ischemic stroke, oraneurysm rupture, forces acting on atherosclerotic plaques or aneurysms,a predicted impact of medical interventional or surgical therapies onintracranial or extracranial blood flow, pressure, wall stress, or brainperfusion. Blood flow, pressure, and wall stress in the intracranial orextracranial arteries, and total and regional brain perfusion may bequantified and the functional significance of disease may be determined.

In addition to quantifying blood flow in the three-dimensional geometricmodel constructed from imaging data (e.g., as described above in step1212), the model may be modified to simulate the effect of progressionor regression of disease or medical, percutaneous, or surgicalinterventions. In an exemplary embodiment, the progression ofatherosclerosis may be modeled by iterating the solution over time,e.g., by solving for shear stress or particle residence time andadapting the geometric model to progress atherosclerotic plaquedevelopment based on hemodynamic factors and/or patient-specificbiochemical measurements. Furthermore, the effect of changes in bloodflow, heart rate, blood pressure, and other physiologic variables onextracranial and/or intracranial artery blood flow or cerebral perfusionmay be modeled through changes in the boundary conditions and used tocalculate the cumulative effects of these variables over time.

Any aspect set forth in any embodiment may be used with any otherembodiment set forth herein. Every device and apparatus set forth hereinmay be used in any suitable medical procedure, may be advanced throughany suitable body lumen and body cavity, and may be used for imaging anysuitable body portion.

It will be apparent to those skilled in the art that variousmodifications and variations can be made in the disclosed systems andprocesses without departing from the scope of the disclosure. Otherembodiments will be apparent to those skilled in the art fromconsideration of the specification and practice of the disclosuredisclosed herein. It is intended that the specification and examples beconsidered as exemplary only, with a true scope and spirit of thedisclosure being indicated by the following claims.

1-184. (canceled)
 185. A method for vascular assessment comprising:receiving a plurality of 2D angiographic images of a portion of avasculature of a subject, and processing said images to produce astenotic model over the vasculature, said stenotic model havingmeasurements of the vasculature at one or more locations along vesselsof the vasculature; obtaining a flow characteristic of the stenoticmodel; and calculating an index indicative of vascular function, based,at least in part, on the flow characteristic in the stenotic model. 186.The method according to claim 185, wherein said measurements of thevasculature are at one or more locations along a centerline of at leastone branch of the vasculature.
 187. The method according to claim 185,wherein said flow characteristic of said stenotic model comprisesresistance to fluid flow.
 188. The method according to claim 187,further comprising identifying in said first stenotic model a stenosedvessel and a downstream portion of said stenosed vessel, and calculatingsaid resistance to fluid flow in said downstream portion; wherein saidindex is calculated based on a volume of said downstream portion, and ona contribution of said stenosed vessel to said resistance to fluid flow.189. The method according to claim 185, wherein said flow characteristicof said stenotic model comprises fluid flow.
 190. The method accordingto claim 185, wherein said stenotic model is a three-dimensional vesseltree.
 191. The method according to claim 190, wherein said vessel treecomprises data pertaining to location, orientation and diameter ofvessels at a plurality of points within said portion of the vasculature.192. The method according to claim 185, wherein said processing saidimages to produce said stenotic model comprises: extending said stenoticmodel by one branch; calculating a new flow characteristic in saidextended stenotic model; updating said index responsively to said newflow characteristic and according to a predetermined criterion; anditeratively repeating said extending, said calculating and saidupdating.
 193. The method according to claim 185, further comprisingprocessing said images to produce a second model over said vasculature,and obtaining a flow characteristic of said second model; wherein saidcalculation of said index is based on the flow characteristic in thestenotic model and on the flow characteristic in the second model 194.The method according to claim 193, wherein said second model is a normalmodel, comprising an inflated vessel replacing a stenotic vessel in thestenotic model.
 195. The method according to claim 193, wherein saidstenotic model is a three-dimensional vessel tree and said second modelis a second three-dimensional vessel tree.
 196. The method according toclaim 193, wherein said flow characteristics of said models comprisefluid flow.
 197. The method according to claim 193, wherein said flowcharacteristics of said models comprise resistance to fluid flow. 198.The method according to claim 193, wherein each of the modelscorresponds to a portion of the vasculature which is between twoconsecutive branches of the vasculature and which includes a stenosis.199. The method according to claim 193, wherein each of the modelscorresponds to a portion of the vasculature which includes a branch ofthe vasculature.
 200. The method according to claim 193, wherein each ofthe models corresponds to a portion of the vasculature which includes astenosis and which extends at least one branch of the vasculature beyondthe stenosis.
 201. The method according to claim 193, wherein each ofthe models corresponds to a portion of the vasculature which includes astenosis and which extends at least three branches of the vasculaturebeyond the stenosis.
 202. The method according to claim 200, whereineach of the models corresponds to a portion of the vasculature whichincludes a stenosis and which extends distally as far as resolution ofsaid images allows.
 203. The method according to claim 193, wherein saidstenotic model corresponds to a portion of the vasculature whichincludes a stenosis, and said second model corresponds to a portion ofthe vasculature which does not include a stenosis and which isgeometrically similar to the stenotic model.
 204. The method accordingto claim 193, wherein said processing said images to produce saidstenotic model and said second model comprises: extending each of themodels by one branch; calculating a new flow characteristic in eachextended model; updating said index responsively to said new flowcharacteristics and according to a predetermined criterion; anditeratively repeating said extending, said calculating and saidupdating.
 205. The method according to claim 193, wherein said index iscalculated based on a ratio of the flow characteristic in the stenoticmodel to the flow characteristic in the second model.
 206. The methodaccording to claim 185, wherein said index is indicative of the need forrevascularization.
 207. The method according to claim 185, furthercomprising obtaining a Fractional Flow Ratio (FFR) based on said index.208. The method according to claim 185, further comprising determining,based on said index, a ratio between maximal blood flow in an area of astenosis and a maximal blood flow in a same area without stenosis. 209.The method according to claim 185, further comprising capturing said 2Dimages.
 210. A non-transitory computer software product, comprising acomputer-readable medium in which program instructions are stored, whichinstructions, when read by a computer, cause the computer to receive aplurality of 2D images of a subject's vasculature and execute the methodaccording to claim
 185. 211. A system for vascular assessmentcomprising: a plurality of imaging devices configured for capturing aplurality of 2D images of a vasculature of a subject; and a computerconfigured for receiving said plurality of 2D images and executing themethod according to claim 185.